Question

The cost of manufacturing of certain items consists of $INR1600$ as overheads, $INR30$ per item as cost of material and the labour costs $INR$ $\frac{x^2}{100}$ for $x$ items produced . how many items must be produced to have a minimum average cost ?

Answer 1

Let the number of units produced is $x$.

Overhead cost $=Rs.1600$

Material cost $=30x$

Labor cost $=\frac{x^2}{100}$

Total cost $=1600+30x+\frac{x^2}{100}$

Divide by $x$ to get average cost.

Average cost $=\frac{1600}{x}+30+\frac{x}{100}$

Now to minimize differentiate and equate to $0$.

$0=\frac{-1600}{x^2}+\frac{1}{100}$

$\therefore$ $\frac{1600}{x^2}=\frac{1}{100}$

$\therefore$ $x^2=160000$

$\therefore$ $x=400$