Popsico is a soda manufacturer. The customers who buy Popsico soda have different tastes y for sugar content ranging from 0 to 1. A total of 100,000 customers are equally distributed along the taste line. Customer is WTP is: 2-2|y-x| for a can of soda with sugar content x. Marginal cost of producing 1 can with any sugar content is 0.1. Assume that the manufacturer serves the entire market. 1.1. Find the profit maximizing choice of x and the price per can if only one type of soda is supplied. 1.2. Suppose now that your product manager suggests replacing the actual product with two new products: light and sweet. Each product type has a fixed cost F = 20,000 for introduction. What must be the sugar contents of the new products and their prices in order to maximize profit? Is this change going to raise Pepsicos profits? 1.3. Prove that, if 90% of consumers had tastes y between 0 and , it would be profitable to produce only one type of soda with x=1/4 rather than two (see point 6.2) covering only half of the taste line