Time and Work
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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

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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.


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