Answer Questions 3 and 4 based on the following linear optimization problem.

Maximize 10X1 + 12X2 + 8X3 + 10X4 Total Profit

Subject to X1 + X2 + X3 + X4 < 200 Resource 1

X1 + 3X2 + 2X3 + 2X4 450 Resource 2

2X1 + X2 + 2X3 + X4 300 Resource 3

And X1, X2, X3, X4 0

Where X1, X2, X3 and X4 represent the number of units of Product 1, Product 2, Product 3 and Product 4 to be manufactured.

The Excel Solver output for this problem is given below.

3. (a) Determine the optimal solution and the optimal value and interpret their meanings.

(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.

4. (a) What are the ranges of optimality for the profit of Product 1, Product 2, Product 3, and Product 4?

(b) Find the shadow prices of the three constraints and interpret their meanings. What are the ranges in which each of these shadow prices is valid?

(c) If the profit contribution of Product 1 changes from $10 per unit to $11 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the sensitivity results given above. Do not solve the problem again).

(d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the sensitivity results given above. Do not solve the problem again).