Solve the following LP
Maximize $5x + $6y
Subject to 2x + 3y ≤ 10 (labor, in hours)
6x + 6y ≤ 36 (materials, in pounds)
7x + 5y ≤ 40 (storage, in square feet)
x, y ≥ 0
a) Write the original optimal solution and objective function value.
b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material?
c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?
d) What is the optimal solution and objective function value if you give up 1 hour of labor and get 1.5 pounds of material?
e) What is the optimal solution and objective function value if you introduce a new product that has a profit contribution of $2? Each unit of this product will use 1 hour of labor, 1 pound of material, and 2 square feet of storage space.
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