Consider the following LP problem, in which X and Y denote the number of units of products X and Y to produce, respectively:

Maximize profit = $4 X + $5 Y

subject to the constraints

X + 2 Y ? 10 (labor available, in hours)

6 X + 6 Y ? 36 (material available, in pounds)

8 X + 4 Y ? 40 (storage available, in square feet)

X , Y ? (nonnegativity)

The Excel Sensitivity Report for this problem is shown in Screenshot 4-9. Calculate and explain what happens to the optimal solution for each of the following situations. Each question is independent of the other questions.

(a) You acquire 2 additional pounds of material.

(b) You acquire 1.5 additional hours of labor.

(c) You give up 1 hour of labor and get 1.5 pounds of material.

(d) The profit contributions for both products X and Y are changed to $4.75 each.

(e) You decide to 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.