1. Independently solve the below LP model two ways both graphically and algebraically using systems of equations. For the graphical approach, label the constraints and the feasible solution space. Find the values of x, y, and the objective function that optimize the model. Show all work.

Maximize Z= 4x + 3y

Subject to 6x +4y 48 pounds

4x +8y 80 hours

x, y 0

2. Given the following linear programming model, solve the model using Excel Solver and answer the questions that follow. Submit your Solver solution (including the sensitivity analysis) and explain each answer,

Maximize Z = 12a + 18b + 15c (Profit for Products A, B, & C)

Subject to

Machine: 5a + 4b + 3c 160 minutes

Labor: 4a + 10b + 4c 288 hours

Materials:2a + 2b + 4c 200 pounds

Product b: b 16 units

a, b, c 0

1) Are any of the constraints binding? If so, which one(s)?

2) If the profit on Product C were changed to $22/unit, what would the value of the decision variables be? The objective function? Explain your thoughts.

3) If the profit on Product A were changed to $22/unit,what would the value of the decision variables be? The objective function? Explain your thoughts.

4) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain your thoughts.

5) If the manager decided that as many as 20 units of Product B could be produced (instead of 16), how much additional profit would be generated?

6) If profit per unit on each product were increased by $1, would the optimal values of the decision variables change? Explain your logic. What would the optimal value of the objective function be?