A firm uses three machines in the manufacture of three products. Each unit of product A requires 3 hours on machine I, two hours on machine II, and one hour on machine III. While each unit of product B requires four hours on machine I, one hour on machine II, and three hours on machine III. While each unit of product C requires two hours on each of the three machines. The contribution margin of the three products is birr 30, birr 40 and birr 35 per unit respectively. The machine hours available on the three machines are 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

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A firm uses three machines in the manufacture of three products. Each
unit of product A requires 3 hours on machine I, two hours on machine
II, and one hour on machine III. While each unit of product B requires
four hours on machine I, one hour on machine II, and three hours on
machine III. While each unit of product C requires two hours on each
of the three machines. The contribution margin of the three products
is birr 30, birr 40 and birr 35 per unit respectively. The machine
hours available on the three machines are 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

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