A manufacturer charges per unit for units that cost to produce. To encourage large orders from distributors, the manufacturer will reduce the price by per unit for orders in excess of units. (For example, an order of units would have a price of per unit, and an order of units would have a price of per unit.) This price reduction is discontinued when the price per unit drops to .
a. Express the price per unit as a function of the order size .
b. Express the profit as a function of the order size .
profit. The unit cost of making the product is 
. She then came up with a formula to determine her selling price at any cost which is unit cost plus 