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Question
The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, whereby marginal cost we mean the instantaneous rate of change of total cost at any level of output.
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Solution
Given that Total coast, C(x) = 0.005x3 − 0.02x2 + 30x + 5000.
We know that marginal cost is the rate of change of total cost with respect to output.
Marginal cost = `(dC)/(dx) = 0.005(3x^2) - 0.02(2x) + 30`
At x = 3 units
`(dC)/(dx) |_(x = 3) = 0.005 (3 xx (3)^3) - 0.02 (2 xx 3) + 30`
=> (dC)/(dx) |_x = 3 = 0.135 - 0.12 + 30 = 30.015
Thus, the required marginal cost when 3 units are produced is Rs 30.015.
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