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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 | 19 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 | 19 Aug, 2014, 10:45: AM

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