PART I (20 Points) On Marginal Analysis of Activities
Your company is producing and selling three products, Alpha, Beta and Gamma. The price, quantity sold and unit variable cost (also known as average variable cost) for each product is listed below.
Alpha Beta Gamma
Price (per unit) $20 $25 $15
Quantity Sold (Q) 10 15 5
Unit Variable Cost (AVC) $18 $23 $10
(a) Assuming that the company has a fixed overhead cost of $70 that must be borne if any of the three products is produced, should the firm “stay in business” or “go out of business”? Explain your answer.
I would “Stay in” or “Go out” (circle one)
(b) If you answer to (a) was “stay in business”, then how high would the fixed overhead have to be in order for the firm to “go out of business? Likewise, if your answer to (a) was “go out of
business”, then how low would the fixed overhead have to be in order for the firm to “stay in
business”? Show your work.
Fixed Overhead would need to be = $___________________________
(c) Assume that products Beta and Gamma are produced using the same facilities so that only one product line can be produced. If you are producing only one of these two, then the fixed
overhead will decrease from $70 to $40. If that is the case, which one, if either, would you
produce? Explain your answer.
I would produce Beta or Gamma (circle one)
(d) In answering (c), you chose to produce Beta or Gamma. To what level would the price of the
excluded produce rise in order for you to change your decision? Explain your answer.
Price would need to rise to = _______________
PART II. (50 points) Optimal Product Mix
Your company produces two products, Model Alpha and Model Beta. These products have profits (or contributions) of $900 and $450 respectively.
Each model is produced in a four process technology. The amount of time used by each model in each process is outlined below. The total amount of time available to produce all models is also listed.
Model Alpha Model Beta Total Time Available
Process 1 18 24 1440
Process 2 8 16 800
Process 3 72 6 576
Process 4 30 15 3750
Using this data, answer the following questions.
(a) You are asked to select the combination of Model Alpha and Model Beta that will maximize
the profitability of your company. Write the linear program that solves this problem.
(b) Using a ruler and/or graph paper, sketch the set that shows the combinations of Model
Alpha and Model Beta that can be produced.
(c) Using ruler and/or graph paper,make a separate sketch that shows a family of “contour
lines” that show various combinations of Model Alpha and Model Beta that will produce
profit of $90,000 and $135,000 respectively.
(d) Find the combination of Model Alpha and Model Beta that maximizes the firm profit. What is firm’s profit at this profit mix (you may do this graphically, or with the Excel Solver)?
Alpha = ________, Beta = _______, Profit = _________
(e) If you could buy extra capacity of Process 1, what is the most that you would be willing to
pay to purchase it? How many units of capacity would you buy? Be sure to show your work
or provide an appropriate explanation.
Most I would be willing to pay = _______________
How many units I would buy = _______________
(f) Suppose that your firm had the ability to produce a new product (Model Gamma). Assume
that this new model used the amount of time for each process listed below. If that is the case,
what would the contribution need to be in order for your firm to produce any units of Model
Contribution from Gamma would need to be _____________________________
PART III. (20 points) A Transportation Problem.
Your company produces products at three manufacturing facilities. The productive
capacity of the three facilities is given below in Table A. These products are shipped to
two retail outlets which sell them to your customers. The demand by customers at each
outlet is given below in Table B. The cost of shipping product from each manufacturing
facility to each outlet is given below in Table C.
Manufacturing Facility Productive Capacity (maximum output)
Factory 1 150
Factory 2 175
Factory 3 175
Retail Outlet Demand (units needed)
Outlet 1 250
Outlet 2 250
From Facility To Outlet Transportation Cost (per unit shipped)
Factory 1 Outlet 1 20
Factory 2 Outlet 1 25
Factory 3 Outlet 1 28
Factory 1 Outlet 2 23
Factory 2 Outlet 2 30
Factory 3 Outlet 2 29
Using the data from the above tables, answer the following questions.
(a) Write the above cost minimization problem as a linear program.
(b) If you are ask to minimize shipment cost, how much product should you ship from each Factoryto each Outlet.
From Facility To Outlet Amount Shipped
Factory 1 Outlet 1 ____
Factory 2 Outlet 1 ____
Factory 3 Outlet 1 ____
Factory 1 Outlet 2 ____
Factory 2 Outlet 2 ____
Factory 3 Outlet 2 ____
(c) Minimum total transportation cost = _______________