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Question
The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is ₹ 120. Find the profit function
Solution
MC = C'(x) = 5 + 0.13x
C(x) = `int "C'"(x) "d"x + "k"_1`
= `int (5 + 0.13x) "d"x + "k"_1`
= `5x + 0.13/2 x^2 + "k"_1`
When quantity produced is zero, fixed cost is 120
i.e When x = 0, C = 120
⇒ k1 = 120
Cost function is 5x + 0.065x2 + 120
Now given MR = R'(x) = 18
R(x) = `int 18 "d"x + "k"_2`
= `18x + "k"_2`
When x = 0
R = 0
⇒ k2 = 0
Revenue = 18x
Profit P = Total Revenue – Total cost
= 18x – (5x + 0.065x2 + 120)
Profit function = 13x – 0.065x2 – 120
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