Question

A company produces two models of products, SUPER and ULTRA. Each SUPER model generates a profit...

  1. A company produces two models of products, SUPER and ULTRA. Each SUPER model generates a profit of $8, and each ULTRA model generates a profit of $5. The table below shows how many minutes are required to produce each model on two different machines with maximum available time. How many products of each model must be produced to maximize profit? How much is the maximum profit?

SUPER

ULTRA

Time Available

Machine 1

3 minutes

2 minutes

360 minutes

Machine 2

2 minutes

1 minute

200 minutes

* Let x be the number of SUPER products and y be the number of ULTRA products.

  1. Write a system of linear inequalities using all the constraints.

  1. Write an objective function (P).

  1. Graph the inequalities and shade the feasible region. Find and list all corners of the feasible region. Be sure to label your scales on each axis.
  1. Evaluate the objective function at each corner and state your final answer in a complete sentence.
Math   Calculus   
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Homework Answers

Answer #1

The system of linear inequalities are

The objective is to maximize profit. So

The graph is as follows

The corners of the feasible region are B(0,180), A(40,120) and C(100,0).

Evaluating the objective function in the corners:

Thus 40 units of SUPER model and 120 units of the ULTRA model must be produced to maximize profit. The maximum profit is $920.

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