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)=2x^{3} -60x^{2} +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

We will find out that using our second derivative test.

For that we need to differentiate this function

We get

Taking 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

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

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