1. (30 points) Consider a manufacturer whose total cost of producing x items is given by c(x)=10000+5x+1/9x^2.
a. What is the average cost function A(x)= c(x)/x?
b. How many items should the manufacturer produce in order to minimize average cost?
c. What is the smallest average cost?
d. Find C’(x).
e. When does C(x) have a critical point? What is the average cost when C(x) has a critical point?