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Dietary optimization
(Maximum Calories and Minimal Cost)
There are six different foods: Bread, Milk, Cheese, Fish, Potato and Yogurt:
| |
Bread |
Milk |
Cheese |
Potato |
Fish |
Yogurt |
| Cost, $ |
2.0 |
3.5 |
8.0 |
1.5 |
11.0 |
1.0 |
| Protein, g |
4.0 |
8.0 |
7.0 |
1.3 |
8.0 |
9.2 |
| Fat, g |
1.0 |
5.0 |
9.0 |
0.1 |
7.0 |
1.0 |
| Carbohydrates, g |
15.0 |
11.7 |
0.4 |
22.6 |
0.0 |
17.0 |
| Calories, Cal |
90 |
120 |
106 |
97 |
130 |
180 |
We have to find a diet that contains not less than 150 calories, not more than
10 g of protein,
not less than 10 g of carbohydrates and not less than 8 g of fat. Also, the diet should have
minimal cost.
In addition the diet should include at least 0.5 g of fish and not more than
1 cups of milk.
Let construct a linear program for this problem:
- We have six unknown variables that define weight of the food.
- There is a lower bound for Fish as 0.5 g.
- There is an upper bound for Milk as 1 cup.
- The objective function is a total cost of the diet.
- We need to minimize the total cost.
- There are four constraints.
The problem has been solved successfully with the following diet:
| Milk |
0.564 cups |
| Cheese |
0.185 g |
| Potato |
0.147 g |
| Fish |
0.5 g |
Bread and Yogurt are excluded from the diet.
The Total Cost is $9.17
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the example in GIPALS format
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