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Question
The total cost C(x) in rupees associated with the production of x units of an item is given by C(x) = 0.007x3 – 0.003x2 + 15x + 4000. Find the marginal cost when 17 units are produced
Solution
C(x) = 0.007x3 - 0.003x2 + 15x + 4000
=> marginal cost = `(dC)/dx`
`= d/dx (0.007 x ^3 - 0.003x ^2 + 15x + 4000)`
= 0.007 × 3x2 - 0.003 × 2x + 15
`∴ (MC)_(x = 17)`
= {0.007 × 3(17)2} - {0.003 × 2(17)} + 15
= 6.069 - 0.102 + 15
= 20.967a
∴ Marginal cost (when x = 17) = 20.967.
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