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{"ops":[{"insert":"A firm uses three machines in the manufacture of three products. Each unit of product A requires 3 hours on machine I, 2 hours on machine II, and one hour on machine III. Each unit of product B requires 4 hours on machine I, one hour on machine II, and 3 hours on machine III, while each unit of product C requires 2 hours on each of the three machines. The contribution margin of the three products is $30, $40, and $35 per unit respectively. The machine hours available on the three machines are 90, 54, and 93 respectively.\nFormulate the above problem as a linear programming problem\nObtain optimal solution to the problem by using the simplex method. Which of the three products shall not be produced by the firm? Why?\nCalculate the percentage of capacity utilization in the optimal solution\nIs the optimal solution degenerate?\n"}]}
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