15) The total cost C(x) in Rupees associated with the production of x units of an
item is given by C ( x) = 0.007 x^3 - 0.003 x^2 + 15 x + 4000

Find the marginal cost when 17 units are produced.

Answers (1)

Marginal cost (MC) = \frac{dC}{dx} 
C ( x) = 0.007 x^3 - 0.003 x^2 + 15 x + 4000
\frac{dC}{dx} = \frac{d(.007x^{3} - .003x^{2}+15x+400)}{dx} = 3\times .007x^{2} - 2\times.003x+15
                                                                                    = .021x^{2} - .006x + 15
Now, at x = 17
MC = .021(17)^{2} - .006(17) + 15
      = 6.069 - .102 + 15
      = 20.967
Hence, marginal cost when 17 units are produced is 20.967

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