Suppose 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, cottage cheese, and popcorn provide 25, 6, and 10 grams of carbohydrates per cup, respectively. Referring to the accompanying table, respond to the following questions:

a. Given that Bill can consume 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?

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Units of food Marginal utilityMarginal utility cups/day)of Rice Krispies Marginal utility cottage cheese of popcom 175 150 125 100 75 50 25 25 72 54 48 36 30 18 90 80 /0 60 50 40 30 20