1. Write down the optimal solution for x1 , x2 , x3 and the corresponding optimal profit z . (5 marks)

2. Management has decided to decrease the price of fertilizer A. The profit contribution will decrease from $50 to $40 for each pound of fertilizer A produced. Will the optimal point change? Why? What is the optimal profit in this case? (5 marks)

3. Instead of decreasing the price of fertilizer A, the management increases the RHS value of the second constraint by 30 units, will the optimal point change? Why? What is the optimal profit in this case? (5 marks)

4. How much would you be willing to pay for an additional unit of Resource 1? Explain. (5 marks)

5. How much would you be willing to pay for an additional unit of Resource 3?

Explain.(5 marks)

Q2 The Total Lawncare Company has to make x1 pounds of fertilizer A, x2 pounds of fertilizer B, and x3 pounds of fertilizer C. The following Linear Programming model has been developed to help Total Lawncare decide the values of x1, x2 and x3 in order to maximize the prot 2 . Maximize z = 50x1 + 20x2 + 30x3 subject to 2x1 + x2 + x3 S 90 (Resource 1) x1 + 2x2 + x3 s 50 (Resource 2) x1 + x2 + x3 3 80 (Resource 3) x1, x2, x3 2 0