# MAT 540 Quiz 1-5. 100/100. Get an A++.

QUIZ 1 1Probabilistic techniques assume that no uncertainty exists in model parameters. 2Fixed cost is the difference between total cost and total variable cost. 3Parameters are known, constant values that are usually coefficients of variables in equations. 4In general, an increase in price increases the break even point if all costs are held constant. 5A continuous random variable may assume only integer values within a given interval. 6If events A and B are independent, then P(A|B) = P(B|A). 7P(A | B) is the probability of event A, if we already know that event B has occurred. 8The purpose of breakÂ]even analysis is to determine the number of units of a product to sell thatwill 9If the price increases but fixed and variable costs do not change, the break even point 10The indicator that results in total revenues being equal to total cost is called the 11A bed and breakfast breaks even every month if they book 30 rooms over the course of amonth. Their fixed cost is \$4200 per month and the revenue they receive from each bookedroom is \$180. What their variable cost per occupied room? 12The expected value of the standard normal distribution is equal to 13The area under the normal curve represents probability, and the total area under the curvesums to 14In a binomial distribution, for each of n trials, the event 15Administrators at a university are planning to offer a summer seminar. The costs of reserving aroom, hiring an instructor, and bringing in the equipment amount to \$3000.Suppose that it costs \$25 per student for the administrators to provide the course materials. Ifwe know that 20 people will attend, what price should be charged per person to breakeven? Note: please report the result as a whole number, rounding if necessary and omittingthe decimal point. 16Administrators at a university will charge students \$158 to attend a seminar. It costs \$2160 toreserve a room, hire an instructor, and bring in the equipment. Assume it costs \$50 per studentfor the administrators to provide the course materials. How many students would have toregister for the seminar for the university to break even? Note: please report the result as awhole number, omitting the decimal point. 17A production run of toothpaste requires a fixed cost of \$100,000. The variable cost per unit is\$3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must bechosen in order to break even at the end of the month? Note: please report the result as awhole number, rounding if necessary and omitting the decimal point. 18Wei is considering pursuing an MS in Information Systems degree. She has applied to twodifferent universities. The acceptance rate for applicants with similar qualifications is 20% forUniversity X and 45% for University Y. What is the probability that Wei will be accepted by atleast one of the two universities? {Express your answer as a percent. Round (if necessary) to thenearest whole percent and omit the decimal. For instance, 20.1% would be written as 20} 19An automotive center keeps tracks of customer complaints received each week. The probabilitydistribution for complaints can be represented as a table (shown below). The random variablexi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.xi 0 1 2 3 4 5 6p(xi) .10 .15 .18 .20 .20 .10 .07What is the average number of complaints received per week? Note: Please report youranswer with two places to the right of the decimal, rounding if appropriate. 20The variance of the standard normal distribution is equal to __________.QUIZ 2 1Probability trees are used only to compute conditional probabilities. 2If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) 3Seventy two percent of all observations fall within 1 standard deviation of the mean if the datais normally distributed. 4The Hurwicz criterion is a compromise between the maximax and maximin criteria. 5The maximin approach involves choosing the alternative with the highest or lowest payoff. 6The minimin criterion is optimistic. 7Both maximin and minimin criteria are optimistic. 8A professor would like to utilize the normal distribution to assign grades such that 5% ofstudents receive Aâs. If the exam average is 62 with a standard deviation of 13, what gradeshould be the cutoff for an A? (Round your answer.) 9The metropolitan airport commission is considering the establishment of limitations on noisepollution around a local airport. At the present time, the noise level per jet takeoff in oneneighborhood near the airport is approximately normally distributed with a mean of 100decibels and a standard deviation of 3 decibels. What is the probability that a randomlyselected jet will generate a noise level of more than 105 decibels? 10The chiÂ]square test is a statistical test to see if an observed data fit a _________. 11The maximin criterion results in the 12A group of friends are planning a recreational outing and have constructed the following payofftable to help them decide which activity to engage in. Assume that the payoffs represent theirlevel of enjoyment for each activity under the various weather conditions.WeatherCold Warm RainyS1 S2 S3Bike: A1 10 8 6Hike: A2 14 15 2Fish: A3 7 8 9What is the conservative decision for this situation? 13A business owner is trying to decide whether to buy, rent, or lease office space and hasconstructed the following payoff table based on whether business is brisk or slow.The maximax strategy is: 14A business owner is trying to decide whether to buy, rent, or lease office space and hasconstructed the following payoff table based on whether business is brisk or slow.The maximin strategy is: 15A brand of television has a lifetime that is normally distributed with a mean of 7 years and astandard deviation of 2.5 years. What is the probability that a randomly chosen TV will lastmore than 8 years? Note: Write your answers with two places after the decimal, rounding off asappropriate. 16A life insurance company wants to update its actuarial tables. Assume that the probabilitydistribution of the lifetimes of the participants is approximately a normal distribution with amean of 71 years and a standard deviation of 3.5 years. What proportion of the planparticipants are expected to see their 75th birthday? Note: Write your answers with two placesafter the decimal, rounding off as appropriate. 17A group of friends are planning a recreational outing and have constructed the following payofftable to help them decide which activity to engage in. Assume that the payoffs represent theirlevel of enjoyment for each activity under the various weather conditions.WeatherCold Warm RainyS1 S2 S3Bike: A1 10 8 6Hike: A2 14 15 2Fish: A3 7 8 9If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4,and 0.4, respectively what is the EVPI for this situation? 18A manager has developed a payoff table that indicates the profits associated with a set ofalternatives under 2 possible states of nature.Alt S1 S21 10 22 Â]2 83 8 5What is the highest expected value? Assume that the probability of S2 is equal to 0.4. 19Consider the following decision tree.What is the expected value for the best decision? Round your answer to the nearest wholenumber. 20The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze(a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available.Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chancethat the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).What is the numerical value of the minimax regret?Quiz 3 1In a linear programming problem, all model parameters are assumed to be known withcertainty. 2A linear programming problem may have more than one set of solutions. 3The following inequality represents a resource constraint for a maximization problem:X + Y . 20 4In minimization LP problems the feasible region is always below the resource constraints. 5If the objective function is parallel to a constraint, the constraint is infea
sible. 6If the objective function is parallel to a constraint, the constraint is infeasible. 7A feasible solution violates at least one of the constraints. 8Decision variables 9The following is a graph of a linear programming problem. The feasible solution space is shaded,and the optimal solution is at the point labeled Z*.The equation for constraint DH is: 10The following is a graph of a linear programming problem. The feasible solution space is shaded,and the optimal solution is at the point labeled Z*.Which of the following points are not feasible? 11In a linear programming problem, the binding constraints for the optimal solution are:5Ã1 + 3Ã2 . 302Ã1 + 5Ã2 . 20Which of these objective functions will lead to the same optimal solution? 12Which of the following could be a linear programming objective function? 13The production manager for the Coory soft drink company is considering the production of 2kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. Toproduce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits fordiet soft drink are \$2.00 per case. What is the objective function? 14Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each bigshelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs\$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelvesthis week, and the warehouse has 18000 cubic feet available for storage. Profit for each bigshelf is \$300 and for each medium shelf is \$150. What is the objective function? 15The linear programming problem:MIN Z = 2Ã1 + 3Ã2Subject to: x1 + 2Ã2 . 205Ã1 + x2 . 404Ã1 +6Ã2 . 60×1 , x2 . 0 , 16Which of the following statements is not true? 17The production manager for the Coory soft drink company is considering the production of 2kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours= 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. Toproduce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits fordiet soft drink are \$2.00 per case. For the production combination of 135 cases of regular and 0cases of diet soft drink, which resources will not be completely used? 18Consider the following minimization problem:Min z = x1 + 2Ã2s.t. x1 + x2 . 3002Ã1 + x2 . 4002Ã1 + 5Ã2 . 750×1, x2 . 0Find the optimal solution. What is the value of the objective function at the optimalsolution? Note: The answer will be an integer. Please give your answer as an integer withoutany decimal point. For example, 25.0 (twenty five) would be written 25 19Solve the following graphicallyMax z = 3Ã1 +4Ã2s.t. x1 + 2Ã2 . 162Ã1 + 3Ã2 . 18×1 . 2×2 . 10×1, x2 . 0Find the optimal solution. What is the value of the objective function at the optimalsolution? Note: The answer will be an integer. Please give your answer as an integer withoutany decimal point. For example, 25.0 (twenty five) would be written 25 20A graphical representation of a linear program is shown below. The shaded area represents thefeasible region, and the dashed line in the middle is the slope of the objective function.What would be the new slope of the objective function if multiple optimal solutions occurredalong line segment AB? Write your answer in decimal notation.QUiz 4 1In a balanced transportation model, supply equals demand such that all constraints can betreated as equalities. 2Fractional relationships between variables are permitted in the standard form of a linearprogram. 3The standard form for the computer solution of a linear programming problem requires allvariables to be to the right and all numerical values to be to the left of the inequality or equalitysign 4Product mix problems cannot have âgreater than or equal toâ (.) constraints. 5In formulating a typical diet problem using a linear programming model, we would expect mostof the constraints to be related to calories. 6In a transportation problem, a demand constraint (the amount of product demanded at a givendestination) is a lessÂ]thanÂ]or equalÂ]to constraint (.). 7Balanced transportation problems have the following type of constraints: 8When systematically formulating a linear program, the first step is 9A systematic approach to model formulation is to first 10In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor stipulatesthat stock 1 must not account for more than 35% of the number of shares purchased. Whichconstraint is correct? 11The owner of Black Angus Ranch is trying to determine the correct mix of two types of beeffeed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essentialingredients are contained in the feed, shown in the table below. The table also shows theminimum daily requirements of each ingredient.IngredientPercent per poundin Feed APercent per poundin Feed BMinimum dailyrequirement(pounds)1 20 24 302 30 10 503 0 30 204 24 15 605 10 20 40The constraint for ingredient 3 is: 12In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to\$50,000 to invest. The stockbroker suggests limiting the investments so that no more than\$10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed350, whichever is more restrictive. How would this be formulated as a linear programmingconstraint? 13The following types of constraints are ones that might be found in linear programmingformulations:1. .2. =3. > 14The production manager for the Softy soft drink company is considering the production of 2kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce aregular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drinkare \$2.00 per case. What is the time constraint? 15Let xij = gallons of component i used in gasoline j. Assume that we have two components andtwo types of gasoline. There are 8,000 gallons of component 1 available, and the demandgasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraintfor component 1. 16In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to\$50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and11%. An appropriate objective function is 17Small motors for garden equipment is produced at 4 manufacturing facilities and needs to beshipped to 3 plants that produce different garden items (lawn mowers, rototillers, leafblowers). The company wants to minimize the cost of transporting items between the facilities,taking into account the demand at the 3 different plants, and the supply at each manufacturingsite. The table below shows the cost to ship one unit between each manufacturing facility andeach plant, as well as the demand at each plant and the supply at each manufacturing facility.What is the demand constraint for plant B? 18Compared to blending and product mix problems, transportation problems are unique because 19Quickbrush Paint Company makes a profit of \$2 per gallon on its oilÂ]base paint and \$3 pergallon on its waterÂ]base paint. Both paints contain two ingredients, A and B. The oilÂ]base paintcontains 90 percent A and 10 percent B, whereas the water
Â]base paint contains 30 percent Aand 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons ofingredient B in inventory and cannot obtain more at this time. The company wishes to uselinear programming to determine the appropriate mix of oilÂ]base and waterÂ]base paint toproduce to maximize its total profit. How many gallons of water based paint should theQuickbrush make? Note: Please express your answer as a whole number, rounding the nearestwhole number, if appropriate. 20Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the qualityof care the pets receive, including well balanced nutrition. The kennelâs cat food is made bymixing two types of cat food to obtain the ânutritionally balanced cat diet.â The data for thetwo cat foods are as follows:Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3ounces of fat per day. What is the cost of this plan? Express your answer with two places to theright of the decimal point. For instance, \$9.32 (nine dollars and thirtyÂ]two cents) would bewritten as 9.32QUIZ 5 1In a mixed integer model, some solution values for decision variables are integer and others areonly 0 or 1. 2If we are solving a 0Â]1 integer programming problem with three decision variables, theconstraint x1 + x2 + x3 . 3 is a mutually exclusive constraint. 3Rounding nonÂ]integer solution values up to the nearest integer value will result in an infeasiblesolution to an integer linear programming problem. 4The solution to the LP relaxation of a maximization integer linear program provides an upperbound for the value of the objective function. 5A conditional constraint specifies the conditions under which variables are integers or realvariables. 6If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3separate constraints in an integer program. 7Max Z = 5Ã1 + 6Ã2Subject to: 17Ã1 + 8Ã2 . 1363Ã1 + 4Ã2 . 36×1, x2 . 0 and integerWhat is the optimal solution? 8Assume that we are using 0Â]1 integer programming model to solve a capital budgeting problemand xj = 1 if project j is selected and xj = 0, otherwise.The constraint (x1 + x2 + x3 + x4 . 2) means that __________ out of the 4 projects must beselected. 9If we are solving a 0Â]1 integer programming problem, the constraint x1 + x2 . 1 is a __________constraint. 10In a __________ integer model, some solution values for decision variables are integers andothers can be nonÂ]integer. 11If we are solving a 0Â]1 integer programming problem, the constraint x1 . x2 is a__________ constraint. 12In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannotbe selected. Which of the alternatives listed below correctly models this situation? 13You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designateeach site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.Restriction 2. Evaluating sites S2 orS4 will prevent you from assessing site S5.Restriction 3. Of all the sites, at least 3 should be assessed.Assuming that Si is a binary variable, write the constraint(s) for the second restriction 14You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designateeach site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.Restriction 2. Evaluating sites S2 orS4 will prevent you from assessing site S5.Restriction 3. Of all the sites, at least 3 should be assessed.Assuming that Si is a binary variable, the constraint for the first restriction is 15The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoffhas 4 different machines that can produce this kind of hose. Because these machines are fromdifferent manufacturers and use differing technologies, their specifications are not the same.Write the constraint that indicates they can purchase no more than 3 machines. 16In a 0Â]1 integer programming model, if the constraint x1Â]x2 = 0, it means when project 1 isselected, project 2 __________ be selected. 17If the solution values of a linear program are rounded in order to obtain an integer solution, thesolution is 18If we are solving a 0Â]1 integer programming problem, the constraint x1 + x2 = 1 is a __________constraint. 19Consider the following integer linear programming problemMax Z = 3Ã1 + 2Ã2Subject to: 3Ã1 + 5Ã2 . 305Ã1 + 2Ã2 . 28×1 . 8×1 ,x2 . 0 and integerFind the optimal solution. What is the value of the objective function at the optimalsolution. Note: The answer will be an integer. Please give your answer as an integer without anydecimal point. For example, 25.0 (twentyÂ]five) would be written 25 20Consider the following integer linear programming problemMax Z = 3Ã1 + 2Ã2Subject to: 3Ã1 + 5Ã2 . 304Ã1 + 2Ã2 . 28×1 . 8×1 , x2 . 0 and integerFind the optimal solution. What is the value of the objective function at the optimalsolution. Note: The answer will be an integer. Please give your answer as an integer without anydecimal point. For example, 25.0 (twentyÂ]five) would be written 25

# MAT 540 Quiz 1-5. 100/100. Get an A++.

QUIZ 1 1Probabilistic techniques assume that no uncertainty exists in model parameters. 2Fixed cost is the difference between total cost and total variable cost. 3Parameters are known, constant values that are usually coefficients of variables in equations. 4In general, an increase in price increases the break even point if all costs are held constant. 5A continuous random variable may assume only integer values within a given interval. 6If events A and B are independent, then P(A|B) = P(B|A). 7P(A | B) is the probability of event A, if we already know that event B has occurred. 8The purpose of breakÂ]even analysis is to determine the number of units of a product to sell thatwill 9If the price increases but fixed and variable costs do not change, the break even point 10The indicator that results in total revenues being equal to total cost is called the 11A bed and breakfast breaks even every month if they book 30 rooms over the course of amonth. Their fixed cost is \$4200 per month and the revenue they receive from each bookedroom is \$180. What their variable cost per occupied room? 12The expected value of the standard normal distribution is equal to 13The area under the normal curve represents probability, and the total area under the curvesums to 14In a binomial distribution, for each of n trials, the event 15Administrators at a university are planning to offer a summer seminar. The costs of reserving aroom, hiring an instructor, and bringing in the equipment amount to \$3000.Suppose that it costs \$25 per student for the administrators to provide the course materials. Ifwe know that 20 people will attend, what price should be charged per person to breakeven? Note: please report the result as a whole number, rounding if necessary and omittingthe decimal point. 16Administrators at a university will charge students \$158 to attend a seminar. It costs \$2160 toreserve a room, hire an instructor, and bring in the equipment. Assume it costs \$50 per studentfor the administrators to provide the course materials. How many students would have toregister for the seminar for the university to break even? Note: please report the result as awhole number, omitting the decimal point. 17A production run of toothpaste requires a fixed cost of \$100,000. The variable cost per unit is\$3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must bechosen in order to break even at the end of the month? Note: please report the result as awhole number, rounding if necessary and omitting the decimal point. 18Wei is considering pursuing an MS in Information Systems degree. She has applied to twodifferent universities. The acceptance rate for applicants with similar qualifications is 20% forUniversity X and 45% for University Y. What is the probability that Wei will be accepted by atleast one of the two universities? {Express your answer as a percent. Round (if necessary) to thenearest whole percent and omit the decimal. For instance, 20.1% would be written as 20} 19An automotive center keeps tracks of customer complaints received each week. The probabilitydistribution for complaints can be represented as a table (shown below). The random variablexi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.xi 0 1 2 3 4 5 6p(xi) .10 .15 .18 .20 .20 .10 .07What is the average number of complaints received per week? Note: Please report youranswer with two places to the right of the decimal, rounding if appropriate. 20The variance of the standard normal distribution is equal to __________.QUIZ 2 1Probability trees are used only to compute conditional probabilities. 2If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) 3Seventy two percent of all observations fall within 1 standard deviation of the mean if the datais normally distributed. 4The Hurwicz criterion is a compromise between the maximax and maximin criteria. 5The maximin approach involves choosing the alternative with the highest or lowest payoff. 6The minimin criterion is optimistic. 7Both maximin and minimin criteria are optimistic. 8A professor would like to utilize the normal distribution to assign grades such that 5% ofstudents receive Aâs. If the exam average is 62 with a standard deviation of 13, what gradeshould be the cutoff for an A? (Round your answer.) 9The metropolitan airport commission is considering the establishment of limitations on noisepollution around a local airport. At the present time, the noise level per jet takeoff in oneneighborhood near the airport is approximately normally distributed with a mean of 100decibels and a standard deviation of 3 decibels. What is the probability that a randomlyselected jet will generate a noise level of more than 105 decibels? 10The chiÂ]square test is a statistical test to see if an observed data fit a _________. 11The maximin criterion results in the 12A group of friends are planning a recreational outing and have constructed the following payofftable to help them decide which activity to engage in. Assume that the payoffs represent theirlevel of enjoyment for each activity under the various weather conditions.WeatherCold Warm RainyS1 S2 S3Bike: A1 10 8 6Hike: A2 14 15 2Fish: A3 7 8 9What is the conservative decision for this situation? 13A business owner is trying to decide whether to buy, rent, or lease office space and hasconstructed the following payoff table based on whether business is brisk or slow.The maximax strategy is: 14A business owner is trying to decide whether to buy, rent, or lease office space and hasconstructed the following payoff table based on whether business is brisk or slow.The maximin strategy is: 15A brand of television has a lifetime that is normally distributed with a mean of 7 years and astandard deviation of 2.5 years. What is the probability that a randomly chosen TV will lastmore than 8 years? Note: Write your answers with two places after the decimal, rounding off asappropriate. 16A life insurance company wants to update its actuarial tables. Assume that the probabilitydistribution of the lifetimes of the participants is approximately a normal distribution with amean of 71 years and a standard deviation of 3.5 years. What proportion of the planparticipants are expected to see their 75th birthday? Note: Write your answers with two placesafter the decimal, rounding off as appropriate. 17A group of friends are planning a recreational outing and have constructed the following payofftable to help them decide which activity to engage in. Assume that the payoffs represent theirlevel of enjoyment for each activity under the various weather conditions.WeatherCold Warm RainyS1 S2 S3Bike: A1 10 8 6Hike: A2 14 15 2Fish: A3 7 8 9If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4,and 0.4, respectively what is the EVPI for this situation? 18A manager has developed a payoff table that indicates the profits associated with a set ofalternatives under 2 possible states of nature.Alt S1 S21 10 22 Â]2 83 8 5What is the highest expected value? Assume that the probability of S2 is equal to 0.4. 19Consider the following decision tree.What is the expected value for the best decision? Round your answer to the nearest wholenumber. 20The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze(a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available.Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chancethat the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).What is the numerical value of the minimax regret?Quiz 3 1In a linear programming problem, all model parameters are assumed to be known withcertainty. 2A linear programming problem may have more than one set of solutions. 3The following inequality represents a resource constraint for a maximization problem:X + Y . 20 4In minimization LP problems the feasible region is always below the resource constraints. 5If the objective function is parallel to a constraint, the constraint is infea
sible. 6If the objective function is parallel to a constraint, the constraint is infeasible. 7A feasible solution violates at least one of the constraints. 8Decision variables 9The following is a graph of a linear programming problem. The feasible solution space is shaded,and the optimal solution is at the point labeled Z*.The equation for constraint DH is: 10The following is a graph of a linear programming problem. The feasible solution space is shaded,and the optimal solution is at the point labeled Z*.Which of the following points are not feasible? 11In a linear programming problem, the binding constraints for the optimal solution are:5Ã1 + 3Ã2 . 302Ã1 + 5Ã2 . 20Which of these objective functions will lead to the same optimal solution? 12Which of the following could be a linear programming objective function? 13The production manager for the Coory soft drink company is considering the production of 2kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. Toproduce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits fordiet soft drink are \$2.00 per case. What is the objective function? 14Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each bigshelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs\$300 and requires 90 cubic feet of storage space. The company has \$75000 to invest in shelvesthis week, and the warehouse has 18000 cubic feet available for storage. Profit for each bigshelf is \$300 and for each medium shelf is \$150. What is the objective function? 15The linear programming problem:MIN Z = 2Ã1 + 3Ã2Subject to: x1 + 2Ã2 . 205Ã1 + x2 . 404Ã1 +6Ã2 . 60×1 , x2 . 0 , 16Which of the following statements is not true? 17The production manager for the Coory soft drink company is considering the production of 2kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours= 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. Toproduce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4minutes and 3 gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits fordiet soft drink are \$2.00 per case. For the production combination of 135 cases of regular and 0cases of diet soft drink, which resources will not be completely used? 18Consider the following minimization problem:Min z = x1 + 2Ã2s.t. x1 + x2 . 3002Ã1 + x2 . 4002Ã1 + 5Ã2 . 750×1, x2 . 0Find the optimal solution. What is the value of the objective function at the optimalsolution? Note: The answer will be an integer. Please give your answer as an integer withoutany decimal point. For example, 25.0 (twenty five) would be written 25 19Solve the following graphicallyMax z = 3Ã1 +4Ã2s.t. x1 + 2Ã2 . 162Ã1 + 3Ã2 . 18×1 . 2×2 . 10×1, x2 . 0Find the optimal solution. What is the value of the objective function at the optimalsolution? Note: The answer will be an integer. Please give your answer as an integer withoutany decimal point. For example, 25.0 (twenty five) would be written 25 20A graphical representation of a linear program is shown below. The shaded area represents thefeasible region, and the dashed line in the middle is the slope of the objective function.What would be the new slope of the objective function if multiple optimal solutions occurredalong line segment AB? Write your answer in decimal notation.QUiz 4 1In a balanced transportation model, supply equals demand such that all constraints can betreated as equalities. 2Fractional relationships between variables are permitted in the standard form of a linearprogram. 3The standard form for the computer solution of a linear programming problem requires allvariables to be to the right and all numerical values to be to the left of the inequality or equalitysign 4Product mix problems cannot have âgreater than or equal toâ (.) constraints. 5In formulating a typical diet problem using a linear programming model, we would expect mostof the constraints to be related to calories. 6In a transportation problem, a demand constraint (the amount of product demanded at a givendestination) is a lessÂ]thanÂ]or equalÂ]to constraint (.). 7Balanced transportation problems have the following type of constraints: 8When systematically formulating a linear program, the first step is 9A systematic approach to model formulation is to first 10In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor stipulatesthat stock 1 must not account for more than 35% of the number of shares purchased. Whichconstraint is correct? 11The owner of Black Angus Ranch is trying to determine the correct mix of two types of beeffeed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essentialingredients are contained in the feed, shown in the table below. The table also shows theminimum daily requirements of each ingredient.IngredientPercent per poundin Feed APercent per poundin Feed BMinimum dailyrequirement(pounds)1 20 24 302 30 10 503 0 30 204 24 15 605 10 20 40The constraint for ingredient 3 is: 12In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to\$50,000 to invest. The stockbroker suggests limiting the investments so that no more than\$10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed350, whichever is more restrictive. How would this be formulated as a linear programmingconstraint? 13The following types of constraints are ones that might be found in linear programmingformulations:1. .2. =3. > 14The production manager for the Softy soft drink company is considering the production of 2kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce aregular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3gallons of syrup. Profits for regular soft drink are \$3.00 per case and profits for diet soft drinkare \$2.00 per case. What is the time constraint? 15Let xij = gallons of component i used in gasoline j. Assume that we have two components andtwo types of gasoline. There are 8,000 gallons of component 1 available, and the demandgasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraintfor component 1. 16In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,an 3 which have selling prices of \$15, \$47.25, and \$110, respectively. The investor has up to\$50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and11%. An appropriate objective function is 17Small motors for garden equipment is produced at 4 manufacturing facilities and needs to beshipped to 3 plants that produce different garden items (lawn mowers, rototillers, leafblowers). The company wants to minimize the cost of transporting items between the facilities,taking into account the demand at the 3 different plants, and the supply at each manufacturingsite. The table below shows the cost to ship one unit between each manufacturing facility andeach plant, as well as the demand at each plant and the supply at each manufacturing facility.What is the demand constraint for plant B? 18Compared to blending and product mix problems, transportation problems are unique because 19Quickbrush Paint Company makes a profit of \$2 per gallon on its oilÂ]base paint and \$3 pergallon on its waterÂ]base paint. Both paints contain two ingredients, A and B. The oilÂ]base paintcontains 90 percent A and 10 percent B, whereas the water
Â]base paint contains 30 percent Aand 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons ofingredient B in inventory and cannot obtain more at this time. The company wishes to uselinear programming to determine the appropriate mix of oilÂ]base and waterÂ]base paint toproduce to maximize its total profit. How many gallons of water based paint should theQuickbrush make? Note: Please express your answer as a whole number, rounding the nearestwhole number, if appropriate. 20Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the qualityof care the pets receive, including well balanced nutrition. The kennelâs cat food is made bymixing two types of cat food to obtain the ânutritionally balanced cat diet.â The data for thetwo cat foods are as follows:Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3ounces of fat per day. What is the cost of this plan? Express your answer with two places to theright of the decimal point. For instance, \$9.32 (nine dollars and thirtyÂ]two cents) would bewritten as 9.32QUIZ 5 1In a mixed integer model, some solution values for decision variables are integer and others areonly 0 or 1. 2If we are solving a 0Â]1 integer programming problem with three decision variables, theconstraint x1 + x2 + x3 . 3 is a mutually exclusive constraint. 3Rounding nonÂ]integer solution values up to the nearest integer value will result in an infeasiblesolution to an integer linear programming problem. 4The solution to the LP relaxation of a maximization integer linear program provides an upperbound for the value of the objective function. 5A conditional constraint specifies the conditions under which variables are integers or realvariables. 6If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3separate constraints in an integer program. 7Max Z = 5Ã1 + 6Ã2Subject to: 17Ã1 + 8Ã2 . 1363Ã1 + 4Ã2 . 36×1, x2 . 0 and integerWhat is the optimal solution? 8Assume that we are using 0Â]1 integer programming model to solve a capital budgeting problemand xj = 1 if project j is selected and xj = 0, otherwise.The constraint (x1 + x2 + x3 + x4 . 2) means that __________ out of the 4 projects must beselected. 9If we are solving a 0Â]1 integer programming problem, the constraint x1 + x2 . 1 is a __________constraint. 10In a __________ integer model, some solution values for decision variables are integers andothers can be nonÂ]integer. 11If we are solving a 0Â]1 integer programming problem, the constraint x1 . x2 is a__________ constraint. 12In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannotbe selected. Which of the alternatives listed below correctly models this situation? 13You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designateeach site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.Restriction 2. Evaluating sites S2 orS4 will prevent you from assessing site S5.Restriction 3. Of all the sites, at least 3 should be assessed.Assuming that Si is a binary variable, write the constraint(s) for the second restriction 14You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designateeach site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.Restriction 2. Evaluating sites S2 orS4 will prevent you from assessing site S5.Restriction 3. Of all the sites, at least 3 should be assessed.Assuming that Si is a binary variable, the constraint for the first restriction is 15The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoffhas 4 different machines that can produce this kind of hose. Because these machines are fromdifferent manufacturers and use differing technologies, their specifications are not the same.Write the constraint that indicates they can purchase no more than 3 machines. 16In a 0Â]1 integer programming model, if the constraint x1Â]x2 = 0, it means when project 1 isselected, project 2 __________ be selected. 17If the solution values of a linear program are rounded in order to obtain an integer solution, thesolution is 18If we are solving a 0Â]1 integer programming problem, the constraint x1 + x2 = 1 is a __________constraint. 19Consider the following integer linear programming problemMax Z = 3Ã1 + 2Ã2Subject to: 3Ã1 + 5Ã2 . 305Ã1 + 2Ã2 . 28×1 . 8×1 ,x2 . 0 and integerFind the optimal solution. What is the value of the objective function at the optimalsolution. Note: The answer will be an integer. Please give your answer as an integer without anydecimal point. For example, 25.0 (twentyÂ]five) would be written 25 20Consider the following integer linear programming problemMax Z = 3Ã1 + 2Ã2Subject to: 3Ã1 + 5Ã2 . 304Ã1 + 2Ã2 . 28×1 . 8×1 , x2 . 0 and integerFind the optimal solution. What is the value of the objective function at the optimalsolution. Note: The answer will be an integer. Please give your answer as an integer without anydecimal point. For example, 25.0 (twentyÂ]five) would be written 25