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Question
The total cost function for the production of x units of an item is given by C = 10 - 4x3 + 3x4 find the
- average cost function
- marginal cost function
- marginal average cost function.
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Solution
Given C = 10 - 4x3 + 3x4
i) Average cost (AC)
`= "C"/x = (10 - 4x^3 + 3x^4)/x`
`= 10/x - 4x^2 + 3x^3`
ii) Marginal Cost (MC) = `"dC"/"dx"`
`= "d"/"dx" (10 - 4x^3 + 3x^4)`
`= -12x^2 + 12x^3`
iii) Marginal Average Cost (MAC)
`= "d"/"dx" ("AC")`
`= "d"/"dx" (10/x - 4x^2 + 3x^3)`
`= - 10/x^2 - 8x + 9x^2`
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