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A business can produce three products, A, B, and C. What is the optimal weekly production plan that maximizes profit? The profits per unit are $25 for A, $ 36 for B, and $ 15 for C. The products need to be assembled and finished. The assembly and finishing times (in hours) for the products are provided in the table. The plant currently has 180 hours of assembly and 240 hours of finishing available per week. Management also wants (i) at least twice as many B produced as A, and (ii) the units of C produced should be at least 10 units more than the units of B produced.
A B C
Assembly 2 2.5 3
Finishing 1.5 3 1.25
(i) Formulate the problem.
(ii) Solve using Excel and answer the following questions based on the sensitivity analysis output.
(ii a) What is the optimal solution? Provide your answer as an instruction to the business.
(ii b) Does the optimal solution change if the profit for unit of A is $22. Explain
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