The objective of a linear programming problem is to maximize 1.50A + 1.50B, subject to 3A + 2B ? 600, 2A + 4B ? 600, 1A + 3B ? 420, and A,B ? 0

a. Plot the constraints on the grid below
c. Identify the feasible region and its corner points. Show your work.
d. What is the optimal product mix for this problem?


The plot and feasible region appear in the graph below. The corner points are (0, 0), (200, 0), (0, 140), and (150, 75). The first three points can be read from the graph axes. The last corner point is the intersection of the equality 2A + 4B = 600 and 3A + 2B = 600. Multiply the first equality by ½ and subtract from the second, leaving 2A = 300 or A = 150. Substituting A = 150 in either equality yields B = 75, which is the optimal product mix for an objective function value of 337.50.

Business

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