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

Answer 1

Answer:

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:

$TC =\ 1,700 + \ 20x$

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:

$P = \ 40x-(\ 1,700 + \ 20x)\\P = \ 20x-\ 1,700$

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

The break-even point occurs when profit is zero:

$0 = \ 20x-\ 1,700\\x=85$

The shoe order must be at least 85 pairs.