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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)=0.005x30.02x2+30x+5000.
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

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Solution

Given that
C(x)=0.005x30.02x2+30x+5000
The marginal cost is the instantaneous rate of change of total cost at any level of output.
Marginal Cost at any x level of output = C(x)
C(x)=0.015x20.04x+30
Marginal Cost when 3 units are produced,
= C(x) at x=3
= C(3)
= 0.015(3)20.04(3)+30
= 0.1350.12+30=30.015

Marginal Cost when 3 units are produced is 30.015.


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