Suppose that a firm makes gears (G) and axles (A). Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s) be written?
A) G + A ≤ 1000
B) .25G + .5A ≤ 1000
C) G ≤ 15 and A ≤ 30
D) .25G + .5A ≥ 1000
E) 15G + 30A ≤ 1000

Question

Quizplus · Accepted Answer

To represent the labor constraint(s), we need to find a formula that relates the amount of labor required to produce gears and axles to the total amount of available labor. Using the information given in the problem, we know that each gear requires 15 minutes of labor, and each axle requires 30 minutes of labor. Let G be the number of gears produced and A be the number of axles produced. Then the total amount of labor required can be written as:

Labor required = 15G + 30A

Since we are told that there are 1000 hours of labor available, we can write the constraint as:

15G + 30A ≤ 1000

Dividing both sides of the inequality by 60, we get:

0.25G + 0.5A ≤ 16.67

This is equivalent to choice B, where we have used decimal values instead of fractions. Choice B is the best option since it correctly limits the total amount of labor used by the production of gears and axles.

Suppose That a Firm Makes Gears (G) and Axles (A)