Answer to Question #298282 in Operations Research for Amare

Question

4. A firm uses three machines in the manufacture of three products. Each unit of product requires 3 hours on machine I, two hours on machine II, and one hour on machine I While each unit of product B requires four hours on machine I, one hour on machine and three hours on machine III. While each unit of product C requires two hours on ea of the three machines. The contribution margin of the three products is birr 30, birr and birr 35 per unit respectively. The machine hours available on the three machines a 90, 54, and 93 respectively.

a. Formulate the above problem as a linear programing model

b. Obtain optimal solution to the problem by using the simplex method. Which of the three products shall not by produced by the firm? Why?

c. Calculate the unused capacity if any

d. What are the shadow prices of the machine hours?