The cost of producing x units of a product is given by C(x)=700+ 80x - 80ln(x), x is greater or equal to 1. Find the minimum average cost.

Answer 1

C ' (x) = 80 - 80(1/x) = 0 for a min

80 = 80/x
1 = 1/x
x = 1

state the conclusion

Answer 2

the average cost is C(x)/x = 700/x + 80 - 80lnx/x
C'(x) = 20/x^2 (4lnx - 39)
C' = 0 at x = e^(39/4) ≈ 17154
C(17154) = 80