Question

a company makes x toys daily at a cost of C(x)=125+30x+2(x to the power of 2/3) dollars. what daily production level will minimize the average cost? (note define average cost as the Total cost divided by the total number of items)



thx

According to your definition
Average Cost = C(x)/x
=125/x + 30 + 2x^(-1/3)

d(Average Cost)/dx = -125/x^2 - (2/3)x^(-4/3)

set this to zero and solve

(I got x=32.75, but x should be a whole number, so x = 33)