A diet is being prepared for the University of Arizona dorms. The objective is t
ID: 352224 • Letter: A
Question
A diet is being prepared for the University of Arizona dorms. The objective is to feed the students at the least cost, but the diet must have between 1,800 and 3,600 calories. No more than 1,600 calories can be starch, no fewer than 450 can be protein, and no more than 310 calories should be fat. The varied diet is to be made of two foods: A and B. Food A costs $2.20 per pound and contains 800 calories, 731 of which are protein and 69 starch. No more than 2 pounds of food A can be used per resident. Food B costs $3.10 per pound and contains 1,000 calories, of which 700 are starch, 190 are protein, and 110 are fat. Write the equations representing this information. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)
(Click to select) Z Calories Calories Starch Protein Fat Amount of A B S B 2 B S BExplanation / Answer
The Given data is summarized as follows:
Food type
A
B
Requirement per diet
Calorie content per pound
800
1000
Minimum – 1800
Maximum – 3600
Starch Content per pound
69
700
Maximum - 1600
Protein content per pound
731
190
Minimum - 450
Fat content per pound
110
Maximum - 310
Cost per pound
$2.20
$3.10
Decision Variable:
For the given situation, decision is regarding how much pound of food A and B should be blended such that requirement are satisfied and total cost of blending is minimized.
Let,
A = pounds of food A to be blended in diet
B = pounds of food B to be blended in diet
The objective is to provide diet to students by blending food A and B such that total cost is minimized. The cost function is given as follows:
Total cost = (pounds of food A purchased x cost per pound of food A) + (pounds of food B purchased x cost per pound of food B)
Objective function is :
Minimize Z = ($2.20)A + ($3.10)B
Subject To:
1
Minimum requirement of Calories
Total calories of blending >= 1800
800A + 1000B >= 1800
2
Maximum requirement of Calories
Total calories of blending <= 3600
800A + 1000B <= 3600
3
Maximum requirement of Starch
Total starch of blending <= 1600
69A + 700B <= 1600
4
Minimum requirement of Protein
Total protein of blending >= 450
731A + 190B >= 450
5
Maximum requirement of fat
Total protein of blending <= 310
0A + 110B <= 310
6
Maximum amount of food A to be feed
Total pounds of A <= 2
A <= 2
7
Non-negative constraint
A, B >= 0
Thus, the formulation is summarized as follows:
Minimize Z = ($2.20)A + ($3.10)B
1
Calories
800A + 1000B >= 1800
2
Calories
800A + 1000B <= 3600
3
Starch
69A + 700B <= 1600
4
Protein
731A + 190B >= 450
5
fat
0A + 110B <= 310
6
amount of food A
1A <= 2
Food type
A
B
Requirement per diet
Calorie content per pound
800
1000
Minimum – 1800
Maximum – 3600
Starch Content per pound
69
700
Maximum - 1600
Protein content per pound
731
190
Minimum - 450
Fat content per pound
110
Maximum - 310
Cost per pound
$2.20
$3.10
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