The O'Neil 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 $1000 for the production setup. The variable cost is $30 per pair, and each pair sells for $40.
a. Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pair 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 be before O'Neil will break even?