Question

A manufacturer estimates that when q units of a certain commodity are produced, the total cost will be

C(x) rand where

C(q) = q2

25 + 80 000 − 104q.

Answer the following questions:

(i) Use marginal analysis to determine the production level at which the cost will be a minimum.

(ii) Determine the minimum cost.

Answer 1

$C(q)=25q^2+80000-104q$

$C'(q)=50q-104=0$

$q=104/50=2.08$

This is production level at which the cost will be a minimum.

The minimum cost is

$C(2.08)=25\times2.08^2+80000-104\times2.08=108.16+80000+216.32=80324.5$