The marginal cost function for production is 10+24 x-3 x². If the total cost of producing one unit is Rs. 25 find the total cost function. [MTP-Oct-18]

Correct Answer is : 4+10x+12x2−x34+10 x+12 x²-x³4+10x+12x2−x3

Correct Answer is : 4+10x+12x2−x34+10 x+12 x²-x³4+10x+12x2−x3

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Integral Calculus

Question : 72 of 73

Marks: +1, -0

10+24 x-3 x^{2}

[MTP-Oct-18]

Solution:

Concept:

Total cost function is the integral of marginal cost function, plus a constant determined by a given condition.

Explanation:

Given marginal cost

MC = 10 + 24x - 3x^2

Integrate to find total cost

TC

\int (10 + 24x - 3x^2) \, dx = 10x + 12x^2 - x^3 + C

Given

TC = 25

when

x = 1

(one unit):

10(1) + 12(1)^2 - (1)^3 + C = 25

10 + 12 - 1 + C = 25 \implies 21 + C = 25 \implies C = 4

Thus,

TC = 10x + 12x^2 - x^3 + 4 = 4 + 10x + 12x^2 - x^3

Answer:

Option A:

4 + 10x + 12x^2 - x^3

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