Question

A manufacturer produces two models of toy airplanes. It takes the manufacturer 20 minutes to assemble model A and 10 minutes to package
it. It takes the manufacturer 25 minutes to assemble model B and 5 minutes to package it. In a given week, the total available time for
assembling is 3000 minutes, and the total available time for packaging is 1200 minutes. Model A earns a profit of $13 for each unit sold and
model B earns a profit of $6 for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each
model should be produced to maximize the profit for the given week?

Answer 1

9514 1404 393

Answer:

  120 units of model A, 0 units of model B

Step-by-step explanation:

Let x and y represent the numbers of model A and model B produced in a week. Then the problem can be summarized as ...

  maximize 13x +6y . . . . . . . . . . profit (dollars)

  subject to the constraints

     20x +25y ≤ 3000 . . . . . . . . assembly minutes

     10x +5y ≤ 1200 . . . . . . . . . . packaging minutes

The doubly-shaded region on the attached graph is the "feasible region" of solutions to the inequalities. The maximum profit can be found by examining the value of the profit function at each of the vertices of the feasible region. The table in the attachment shows the result.

Profit is maximized by production of 120 units of model A and 0 units of model B.

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The maximum profit is $1560 per week.