Question (3): Given the following formulation, answer thebelow questions: (8 marks)

Decision variables: let x = number of units of product 1 to produce.

let y = number of units of product 2 to produce.

Objective function: Maximize z = x + 2y.

Subject to:

x + y 12 (resource A)

x 8 (resource B)

y 6 (resource C)

x and y 0

Answer the following questions based on the above data:

a. What is the optimal point? (Dont show me your graph here in the paper. Write the optimal point only in the answer) (2 marks)

b. Suppose that a technical breakthrough just occurred that raised the profit per product 2 (Y) from $2 to $12. Is the solution still optimal? Why? (4 marks)

c. Suppose that another technical breakthrough just occurred that raised the profit per product 1 (X) to $6. Is the solution still optimal? Why? (4 marks)