# LoTech Manufacturing produces four different products. Each product requires material, labor, and ma

LoTech Manufacturing produces four different products. Each product requires material, labor, and machine time. The optimal combination of the four products is limited by the constraints of availability for these three resources. The formulation of the linear programming production problem is:Maximize Z = 12×1 + 10×2 + 15×3 + 11×4 (objective function for profit)Subject to the following constraints:Material: 5×1 + 3×2 + 4×3 + 2×4 ? 240 poundsMachine time: 6×1 + 8×2 + 2×3 + 3×4 ? 240 hoursLabor: 2×1 + 3×2 + 3×3 + 2×4 ? 180 hoursNonnegativity: x1, x2, x3, x4 ? 0Where: x1 = quantity of Product 1 producedx2 = quantity of Product 2 producedx3 = quantity of Product 3 producedx4 = quantity of Product 4 produced Use Excel and Solver to find the optimal solution for the production problem.Include your interpretation of the results by stating:How many of each product will be produced?What is the profit for the optimal solution?