EXAMPLE 2.1 The Best Price?

Price is important to consumers and, therefore, to retailers. Sales of an item typically increase as its price falls, except for some luxury items, where high price suggests exclusivity. The seller's profits for an item often increase as the price is reduced, due to increased sales, until the point at which lower profit per item cancels rising sales. Thus, a retail chain introduces a new TV that can respond to voice commands at several different price points and monitors sales. The chain wants to discover the price at which its profits are greatest. Price is the explanatory variable, and total profit from sales of the TV is the response variable.