How many units of each product should be produced in each shift to maximize the company's profit? (x

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Angnyvrqc

Mathematics

Question Description

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $4/unit of Product A and a profit of $7/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? (x, y) =

What is the optimal profit? (Round your answer to the nearest whole number.) $

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Explanation & Answer

Thank you for the opportunity to help you with your question!

This is a type of problem called "linear programming," where you typically plot a system of inequalities (each of which represents a bound on the production of goods) and then test specific values to figure out how to maximize or minimize a company's profits or costs.



STEP 1: Define variables

Here, your variables are number of units of Product A and number of units of Product B:

x = # Product A
y = # Product B
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