Probem53+Hannah+N.,+Susie,



A) The average cost per unit is c(x) = C(x)/x

-The marginal cost is the derivative of the cost function the marginal cost is C'(x)

prove that C'(x) = the average cost

The minimum average cost = the derivative of the average cost function set equal to zero = marginal cost

c'(x) = xC'(x) - C(x) / x^2 0 = xC'(x) - C(x) C(x) = xC'(x) C(x)/x = C'(x)

I disagree with part b above -- the average cost function is c(x)=16,000x^(-1) + 200 + 4x ^(1/2). You are looking for the minimum value of this fucntion, so it is this fucntion of which you must take the derivative.