Suppose Bill is on a low-carbohydrate diet. He can eat only three foods: Rice Kr

Question

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:

Units of Food (cups/day) Marginal utility of Rice Krispies Marginal utility of cottage cheese Marginal utility of popcorn
1 175 72 90
2 150 66 80
3 125 60 70
4 100 54 60
5 75 48 50
6 50 36 40
7 25 30 30
8 25 18 20

Given that Bill can consume only 167 grams of carbohydrates daily, how many cups of each food will he consume daily? Show your work.

Explanation / Answer

marginal utilities is how much you get for each unit it in this case think of it as bill "happiness" and he wants to be the most happy

You want to start eating the food with the most marginal utility per gram

1 175 72 90
RK 175/25=7 per gram
CC 72/6= 12 per gram
PC 90/10= 9 per gram

so you want to start eating cottage cheese until marginal utility less per gram then another food
calulating the MU for the rest of the chart

1 7 12 9
2 6 11 8
3 5 10 7
4 4 9 6
5 3 8 5
6 2 6 4
7 2 5 3
8 2 3 2

MU of CC equal that of the popcorn after 4 serves of CC (6*4=24 g) so you swich to eating popcorn

MU of popcorn equal that of the CC after 1 popcorn (24+10*1=34 g) so you swich back to CC

MU of popcorn at 2 serving and CC at 5 serving are the same so eat one of each (34+6+10=50g)

MU of RK&PC higher then CC 5th serving so eat one of each (50+25+10=85g)

and so on...

Basicly when the MU is less then another food switch take the other food choice

Final answer should be 3 PC, 7 CC, 5 PP with the last unit of each providing 5 MU

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