The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $2000 for the production setup. The variable cost is $60 per pair, and each pair sells for $80.
a. Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pairs of shoes.
b. Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes.
c. How large must the shoe order be before O'Neill will break even?