Question

chicken can eat only three foods: diet rich in proteins, diet rich in fats and mix of proteins and vitamins. The total utilities for each diet are tabulated below. The chicken is allowed only 167 grams of carbohydrates daily. The three diets have a combination of 25 grams of protein, 6 grams of fats and 10 grams of proteins and vitamins, respectively. Referring to the table respond to the following questions: (a) Given that the chicken birds can consume 167 grams of proteins daily, how many cups of 3. Suppose yummy chicken nutritionist is preparing chicken feed diet for the chicken. The each food will he consume daily? Show your workings (b) Suppose the nutritionist suggests that chicken birds are to be fed, to further reduce their n intake to 126 grams per day. What combination will be suggested by the protei nutritionist? Table 3: Marginal benefit of diet mix for yummy chicken Units of Marginal productbenefit of of rich in fats benefit cups /day Protein rich Marginal benefit Marginal proteins and vitamins 90 80 70 60 50 40 30 20 175 150 125 100 72 2 4 575 6 7 60 54 48 36 30 18 50 25 (10 marks) DAYS ECO6001 Page 3 of 4

Answer 1

answer:

Part A)

Given Maximum carbohydrates intake is 167 grams per day

1 cup of diet rich protein (A) = 25 grams of protein

1 cup of diet fats (B)= 6 grams of fats

1 cup of mix of  proteins and Vitamins (C)= 10 grams of proteins and Vitamins

Since we need to maximize our Marginal benefits

Since 4 cups of A has marginal benefits is 100 which is greater maximum marginal benefits of other two diets.so we will give 4 cups of A which has 4*25=100 grams of protein

For 5th cup we will choose from diet C because 1st cup of diet C has greater marginal benefits compare to 5th cup of A and 1st of cup of B. so total intake =100+10=110

For 6th cup we will choose from diet C because 2nd cup of diet C has greater marginal benefits compare to 5th cup of A and 1st of cup of B. so total intake =110+10=120

For 7th cup we will choose from diet A because 5th cup of diet A has greater marginal benefits compare to 3rd cup of C and 1st of cup of B. so total intake =120+25=145

For 8th cup we will choose from diet B because 1st cup of diet B has greater marginal benefits compare to 6th cup of A and 3rd of cup of C. so total intake =145+6=151

For 9th cup we will choose from diet C because 3rd cup of diet C has greater marginal benefits compare to 6th cup of A and 2nd of cup of B. so total intake =151+10=161

For 10th cup we will choose from diet B because 2nd cup of diet B has greater marginal benefits compare to 6th cup of A and 4th of cup of C. so total intake =161+6=167

so for 167 gram of intake we will use 5 cups of diet rich protein, 3 cups of  mix of  proteins and Vitamins and 2 cups of diet fats.

Part B)

Given Maximum carbohydrates intake is 126 grams per day

1 cup of diet rich protein (A) = 25 grams of protein

1 cup of diet fats (B)= 6 grams of fats

1 cup of mix of  proteins and Vitamins (C)= 10 grams of proteins and Vitamins

Since we need to maximize our Marginal benefits

Since 4 cups of A has marginal benefits is 100 which is greater maximum marginal benefits of other two diets.so we will give 4 cups of A which has 4*25=100 grams of protein

For 5th cup we will choose from diet C because 1st cup of diet C has greater marginal benefits compare to 5th cup of A and 1st of cup of B. so total intake =100+10=110

For 6th cup we will choose from diet C because 2nd cup of diet C has greater marginal benefits compare to 5th cup of A and 1st of cup of B. so total intake =110+10=120

for 7 th cup we will choose from diet B instead of diet of A(despite diet A has higher marginal benefits) because we need to only give 126 grams of intake.If we diet A then total intake will be 120+25=145 grams but we need only 126 grams of intake.

So total intake=120+6=126 grams

So for 126 gram of intake we will use 4 cups of diet rich protein, 2 cups of  mix of  proteins and Vitamins and 1 cups of diet fats.