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Question
NARRBEGIN: SA_114_120A chemical manufacturer produces two products, chemical X and chemical Y. Each product is manufactured by a two-step process that involves blending and mixing in machine A and packaging on machine B. Chemical X provides a $60/unit contribution to profit, while Chemical Y provides a $50 contribution to profit. The processing times for the two products on the mixing machine (A) and the packaging machine (B) are as follows:
| Product | Machine A (hours) | Machine B (hours) |
| Chemical X | 2 | 3 |
| Chemical Y | 4 | 2 |
NARREND
(A) Write out algebraic expressions for all of the constraints in this problem.
(B) Construct a graph of the feasible region for this problem, given the constraints you identified in (A).
(C) Describe how you would find the location of the optimal solution in the feasible region you graphed in (B).
(D) Use the procedure you described in (C) to identify the optimal production plan. Confirm your solution using Solver. What is the maximized profit?
(E) What constraints are binding on the optimal solution? Use your graphical solution to explain your answer.
Answer
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