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 $1700 for the production setup. the variable cost is $20 per pair, and each pair sells for $40.

TC = $1,700 + $20x

P = $20x - $1,700

x = 85

Explanation:

Develop a mathematical model for the total cost of producing x pairs of shoes.

The total cost of producing x pairs is given by the fixed cost of $1700 added to a variable cost of $20 per pair. For x pairs:

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

Total profit is given by Revenue from sales minus total costs (found on the previous item). Revenue is $40 per pair. The profit function is:

How large must the shoe order be before O'Neill will break even?

The break-even point occurs when profit is zero:

The shoe order must be at least 85 pairs.