Bill is on a low-carbohydrate diet. He can eat only three foods: Rice Krispies, cottage cheese, and popcorn. The marginal utilities for each food are tabulated below. Bill is allowed only 167 grams of carbohydrates daily. Rice Krispies (RK), cottage cheese (CC), and popcorn (PC) provide 25, 6, and 10 grams of carbohydrates per cup, respectively. Units of food MU of RK MU of CC MU of PC (cups/day) 1 175 72 90 2 150 66 80 3 125 60 70 4 100 54 60 5 50 75 50 25 25 48 36 40 30 20 7 30 8 18 Referring to the accompanying table, respond to the following questions: a. Given that Bill is allowed only 167 grams of carbohydrates daily, how many cups of each food will he consume daily? Show your work. b. Suppose Bill's doctor tells him to further reduce his carbohydrate intake to 126 grams per day. What combination will he consume?