CBSE Class 12 Math 2018 Solved Paper

Question : 8

Total: 29

The total cost C(x) associated with the production of x units of an item is given by
C(x) = 0.005 x3 – 0.02 x2 + 30 x + 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.

Solution:

Given C(x) = 0.005 x3 – 0.02 x2 + 30 x + 5000
Marginal cost is the rate of change of total cost with respect to output.
⇒ Marginal cost =

⇒ Marginal cost = 0.005 (3x2) - 0.02 (2x) + 30 = 0.015 x2 - 0.04 x + 30
Marginal cost at x 3
⇒ Marginal cost = 0.015 × 32 - 0.04 × 3 + 30
⇒ Marginal cost 30.015
Therefore Marginal cost is Rs. 30.015.

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