Aptitude 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.