A small shoe company can produce between 100 and1000 pairs of shoes per day. The cost of...

A small shoe company can produce between 100 and1000 pairs of shoes per day. The cost of producing x pairs of shoes, for 100 ≤ x ≤ 1000, is given by

If x pairs of shoes are sold, then the price per pair that the company will receive is given by

a. Estimate the number of pairs of shoes that should be produced if the average cost per unit is to be a minimum.

b. Estimate the number of pairs of shoes that should be produced in order to maximize the profit.