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Question
The marginal cost function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions
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Solution
MC = `300 x^(2/5)` and fixed cost k = 0
Total cost t = `int"MC" "d"x`
C = `int300 x^(2/5) "d"x`
= `300 (x^(2/5 + 1))/((2/5 + 1)) + "k"`
C = `300[x^(7/5)/((7/5))] + 0`
∴ C = `1500/7 x^(7/5)`
Average cost A.C = `"C"/x = (1500/7 x^(7/5))/x`
A.C = `1500/7 x^(7/5 - 1)`
∴ A.C = `1500/7 x^(2/5)`
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