Kellpost Cereal Company sells four products: (1) Special L (a low-calorie, high-nutrition cereal); (2) Corn Bran (another low-calorie, high-nutrition cereal); (3) Admiral Smacks (a sugary cereal pitched at the children’s market); and (4) Honey Pops (another sweet cereal pitched at the children’s market). Kellpost has sufficient production capacity to produce a total of 10,000 boxes of cereal per month. For each of the past 16 months, Kellpost has kept track of the price and sales of each product. (These data are listed in the file P07_72.xlsx.) Market executives believe that Special L and Corn Bran might be substitutes for each other, as might be Admiral Smacks and Honey Pops. For example, this means that an increase in the price of Special L might raise the sales of Corn Bran. The variable cost of bringing a box of each cereal to market is as follows: Special L, $2.00; Corn Bran, $2.20; Admiral Smacks, $2.30; Honey Pops, $2.40.

a. Use the given information to determine the price for each cereal that will enable Kellpost to maximize profits.

b. Now suppose that Kellpost can increase its monthly production capacity. The cost (per year) of doing this is $20,000 per 1000 boxes of added monthly capacity. Can you determine an optimal capacity level?