Consider the following linear programming formulation: Min 5x + 2y Subject to (1) 3x + 6y ≥ 18 (2) 5x + 4y ≥ 20 (3) 8x + 2y ≥ 16 (4) 7x + 6y ≤ 42 (5) x, y ≥ 0 a. Solve the problem graphically. Specifically, show each constraint and the feasible region, draw an objective function line and identify an optimal point (the solution). When reporting the optimal solution and the corresponding objective function value, you may estimate the optimal x and y values from the graph.
1. Consider the following linear programming formulation: Min 5x + 2y
Subject to (1) 3x + 6y ≥ 18
(2) 5x + 4y ≥ 20
(3) 8x + 2y ≥ 16
(4) 7x + 6y ≤ 42
(5) x, y ≥ 0
a. Solve the problem graphically. Specifically, show each constraint and the feasible region, draw an objective function line and identify an optimal point (the solution). When reporting the optimal solution and the corresponding objective function value, you may estimate the optimal x and y values from the graph.
b. What are the optimal values of x and y, using the solver add-in? What is the corresponding value of the objective function?
c. How many extreme points does the feasible region have? Enumerate them. Hint: It's from the graph.
d. Change the objective function to 15x + 12y.. What is the new optimal solution(s)?
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