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Question
The marginal cost function of a commodity is given by MC = `14000/sqrt(7x + 4)` and the fixed cost is ₹ 18,000. Find the total cost and average cost
Solution
The marginal cost function of a commodity
Mc = `14000/sqrt(7x + 4)`
= `14000 (7x + 4)^((-1)/2)`
Fixed cost k = ₹ 18,000
Total cost function C = `int ("M.C") "d"x`
= `int 14000 (7x + 4)^((-1)/2) "d"x`
= `14000 [(7x + 4)^((-1)/2 + 1)/(((-1)/2 + 1) xx (7))] + "k"`
= `14000 [(7x + 4)^(1/2)/((7/2))] + 18000`
= `14000 xx 2/7 xx (sqrt(7x + 4)) + 18000`
∴ Total cost C = `4000 [sqrt(7x + 4)] + 18000`
Average cost A.C = `("C"(x))/x`
= `(4000[sqrt(7x + 4)] + 18000)/x`
A.C = `4000/x sqrt(7x + 4) + 18000/x`
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