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 = 12x1 + 10x2 + 15x3 + 11x4 (objective function for profit)
Subject to the following constraints:
Material: 5x1 + 3x2 + 4x3 + 2x4 ? 240 pounds
Machine time: 6x1 + 8x2 + 2x3 + 3x4 ? 240 hours
Labor: 2x1 + 3x2 + 3x3 + 2x4 ? 180 hours
Nonnegativity: x1, x2, x3, x4 ? 0
Where: x1 = quantity of Product 1 produced
x2 = quantity of Product 2 produced
x3 = quantity of Product 3 produced
x4 = 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?