Question

A company makes two models of light fixtures, A and B, each of which must be assembled and packed. The time required to assemble model A is 12 minutes, and model B takes 18 minutes. It take 2 minutes to package model A and 1 minute to package model B. Each week there are available 240 hours of assembly time and 20 hours for packaging. If model A sells for $1.50 and model B sells for $1.70, how many of each model should be made to obtain the maximum weekly income? What is the maximum weekly income?

Answer 1

To find the maximum weekly income, we can use a linear programming approach. Let's define the variables:

- Let x be the number of model A light fixtures to be made.

- Let y be the number of model B light fixtures to be made.

We need to maximize the weekly income, which can be calculated as follows:

Income = (selling price of model A * number of model A) + (selling price of model B * number of model B)

Subject to the following constraints:

- Assembly time constraint: 12x + 18y ≤ 240 hours

- Packaging time constraint: 2x + y ≤ 20 hours

- Non-negativity constraint: x ≥ 0, y ≥ 0

Now we can solve this linear programming problem to find the optimal values of x and y that maximize the weekly income.