# Moderate Time and Work Solved QuestionAptitude Discussion

 Q. Suppose $q$ is the number of workers employed by Simplex Ltd. for one of its projects. The average cost of production $c$ is given by (c=dfrac{q^2}{3}+dfrac{5q}{2}-150+dfrac{75}{q}) In the interest of the company, it should employ __________ workers.
 ✖ A. 5 ✖ B. 4 ✖ C. 7 ✔ D. 10

Solution:
Option(D) is correct

The average cost of production $c$ is a function of a single variable $q$, the number of workers employed.

Hence the total cost of production is given by the product  $c×q=T$, say:

$T=c\times q=q\left(\dfrac{q^2}{3}+\dfrac{5q}{2}-150+\dfrac{75}{q}\right)$

$\dfrac{\partial T}{\partial q}=0$

$\Rightarrow q=10$

Hence, 10 workers should be employed.