please answer letter e to i and state the coresponding solution to the letter.

MDW Manufacturing produces two products, each of which must be processed on three machines. The contribution per unit on the two products is Php240.00 and Php300.00, respectively. Product 1 requires 4 hours processing time on machine A, 8 hours on machine B, and 2 hours on machine C. The processing times for product 2 on three machines are 6 hours, 4hours, and 3 hours, respectively. The machine hour capacities for the three machines in the incoming month are 240, 240 and 150 hours for machine A, B and C, respectively.

1. a) Formulate the LP model.

2. b) Solve the LP using the simplex technique

3. c) Specify the optimal solution and the z-value.

4. d) Over what range of the RHS values is each shadow price valid?

5. e) What range of contribution per unit on products 1 and 2 will the current product mix

   remain optimal?

6. f) Due to a rise in material costs, the contribution per unit on product 1 decreases to

   Php210.00. How does this affect the optimal product mix? What about the monthly

   profit?

7. g) Suppose the contribution per unit on product 2 increases to Php330.00 due to the

   successful application of a new production process for that product. How does this affect

   the optimal product mix? What about the monthly profit?

8. h) Suppose the machine hour capacity of machine A can be increased to 274 hours per

   month at a total monthly cost of Php1300.00. Would you recommend that MDW

   undertake the expansion?

9. i) Suppose management can increase the machine-hour capacity of machine B to 350 hours

   at a total monthly cost of Pjp880.00. Should the expansion be undertaken?