The total cost C ( x ) in Rupees associated with the production of x units of an item is given by Find the marginal cost when 17 units are produced.

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Solution

The total cost C( x ) Rs associated with the production of x units is given by,

C( x )=0.007 x 3 −0.003 x 2 +15x+4000

Marginal cost is the rate of change of total cost with the output.

The marginal cost is MC.

According to the given condition,

MC= dC dx = d dx ( 0.007 x 3 −0.003 x 2 +15x+4000 ) =3×0.007 x 2 −2×0.003x+15 =0.021 x 2 −0.006x+15 (1)

Substitute the value of x as 17 in equation (1).

MC=0.021 ( 17 ) 2 −0.006( 17 )+15 =0.021×289−0.006×17+15 =6.069−0.102+15 =20.967

Thus, the marginal cost of 17 units produced is Rs 20.967.

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