Gellogg, a cereal brand, is trying to capture the most of market demand by using a price discrimination strategy. The brand produces Taro Flakes, a breakfast cereal popular for all ages. However, it produces different packages for different market segments: children (segment 1), young-adult (segment 2), and elderly (segment 3). The market demands for those three segments are as follows: Q = 15 3 1 Q3 = 12 -- 4 Q = 21 1 2 -P 1 -5P 1 - 4 -P3 6 The total cost of the firm is C = 30 + 15Q, where Q = Q + Q2 + Q3. Based on above information: i. Write the profit function (Hint: it is a function of Q, Q2, and Q3). ii. What is the profit-maximizing quantities of Q, Q2, and Q3? iii. Show that your answers in (ii) are indeed maximizing the profit.