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Question
Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
Solution
Total cost function, C = 5x3 + 2x2 + 7
Average cost = `"C"/x`
=`(5x^3 + 2x^2 + 7)/x`
= 5x2 + 2x + `7/x`
When x = 4,
Average cost = 5(4)2 + 2(4) + `7/4`
= 80 + 8 + `7/4`
= `(320 + 32+ 7)/4`
= `359/4`
Marginal cost = `("dC")/("d"x)`
=`"d"/("d"x)(5x^3 + 2x^2 + 7)`
= `5"d"/("d"x) (x^3) + 2"d"/("d"x)(x^2) + "d"/("d"x)(7)`
= 5(3x2) + 2(2x) + 0
= 15x2 + 4x
When x = 4, Marginal cost = `(("dC")/"dx")_ (x = 4)`
= 15(4)2 + 4(4)
= 240 + 16
= 256
∴ the average cost and marginal cost at x = 4 are `359/4` and 256 respectively.
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