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.

Answer 1

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.