Consider the following linear programming model.

Max 12x1 +18x2 +15x3

S.T.

5x1 + 4x2 + 3x3 <= 160 minutes (machine constraint)

4x1 +10x2 + 4x3 <= 288 hours (labor constraint)

2x1 +2x2 + 4x3 <= 200 pounds (materials constraint)

x2 <= 16 units (product 2 constraint)

x1, x2, x3 >= 0

(xi = quantity of product I to make, i = 1,2,3)

Note: You will need to use Excel Solver for this problem

1. (10 pts.) Find the optimal solution of this LP problem.
2. (5 pts.) Are any constraints binding? If so, which one(s)?
3. (5 pts.) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain.
4. (5 pts.) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain.
5. (5 pts.) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain.
6. (5 pts.) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated?
7. (5 pts.) If profit per unit on each product increased by $1, would the optimal values of the decision variables change? Explain. What would the optimal value of the objective function be?