Suppose a company manufactures x units.

And the cost of manufacturing these x units comes out to be a cost function given as c(x)=2x3 -60x2 +1500. Definitely the company would like to minimise its cost to attain maximum profit. So here we would like to know how many units should be manufactured to get minimum cost,

Asked by Topperlearning User | 19th Aug, 2014, 08:45: AM

Expert Answer:

We will find out that using our second derivative test.

For that we need to differentiate this function

We get dc over dx equals 6 straight x squared minus 120 straight x

Taking dc over dx equals 0 to find extreme points

            6x(x - 20)=0

Since x≠0 because x=0 means no production so we take x=20.

Now, to check whether this will maximise or minimise cost. We need to find the second derivative, which is fraction numerator straight d squared straight c over denominator dx squared end fraction equals 12 straight x minus 120

This second derivative at x=20 is

            12 x 20 – 120 = 240 – 120 = 120

which is positive.

This indicates that x=20 is a point of local minima.

Hence, we can say cost is minimum when 20 units of items are produced.

Answered by  | 19th Aug, 2014, 10:45: AM