A manufacturing firm produces two products. Each product must go through an assembly process and a finishing process. The product is then transferred to the warehouse, which has space for only a limited number of items. The following linear programming model has been developed for determining the quantity of each product to produce in order to maximize profit:
Maximize Z = 30x1 + 70x2 (profit, $)
Subject to
4x1 + 10x2 ≤ 80 (assembly, hours)
14x1 + 8x2 ≤ 112 (finishing, hours)
x1 + x2 ≤ 10 (inventory, units)
x1, x2 ≥ 0
a. Solve this model graphically.
b. Assume that the objective function has been changed to
Z = 90x1 +70x2. Determine the slope of each objective function and discuss what effect these slopes have on the optimal solution.