company manufactures two products X1 and X2 on three machines A, B, and C. X1 require 1 hour on machine A and 1 hour on machine B

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1. A company manufactures two products X1 and X2 on three machines A, B, and C. X1 require 1 hour on machine A and 1 hour on machine B and yields a revenue of Br.3/-. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of Br. 5/-. In the coming planning period the available time of three machines A, B, and C are 2000 hours, 1500 hours and 600 hours respectively. Formulate a model that helps to find the optimal product mix.

 

2. Dorian makes luxury cars and jeeps for high-income men and women. It wishes to advertise with 1 minute spots in comedy shows and football games. Each comedy spot costs $50K and is seen by 7M high-income women and 2M high-income men. Each football spot costs $100K and is seen by 2M high-income women and 12M high-income men. How can Dorian reach 28M high-income women and 24M high-income men at the least cost? Formulate the model that helps to solve the problem.

3. A factory manufactures two products A and B on three machines X, Y, and Z. Product A requires 10 hours of machine X and 5 hours of machine Y a one our of machine Z. The requirement of product B is 6 hours, 10 hours and 2 hours of machine X, Y and Z respectively. The profit contribution of products A and B is Br. 23/– per unit and Br. 32/– per unit respectively. In the coming planning period the available capacity of machines X, Y and Z are 2500 hours, 2000 hours and 500 hours respectively. Formulate a model that helps to find the optimal product mix for maximizing the profit.

4. Solve the following model using the graphical method

Min z = 50x1 + 100x2 s.t.

7x1 + 2x2 ≥ 28

2x1 + 12x2 ≥ 24

x1, x2 ≥ 0

5. Given the following model:

Maximize Z = 15x1 + 45x2 s.t.

1x1 + 16x2 ≤ 240

5x1 + 2x2 ≤ 162

0x1 + 1x2 ≤ 50 x1, x2 ≥ 0

Required:

A. Find the optimum solution to the problem using simplex method

B. If Zmax and c2 is kept constant at 45, find how much c1 can be changed without affecting then optimal solution. (Hint: find the range of optimality for coefficient of objective function.)

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