The O\'Neill Shoe Manufacturing Company will produce a special-style shoe if the

Question

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 $1300 for the production setup. The variable cost is $20 per pair, and each pair sells for $30.

Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pairs of shoes. Express your answer in terms of x.

TC =

Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes. Express your answer in terms of x.

P =

How large must the shoe order be before O'Neill will break even? Round your answer to the nearest whole number.

x =

Explanation / Answer

TC = 1300 + 20x

P = 30x - (1300 + 20x)
= 10x - 1300

for breakeven
P = 0
10x = 1300
x = 130

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