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Linear Programming Dietary optimization (Maximum Calories and Minimal Cost)

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linear programming GIPALS Start

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

linear programming GIPALS Start

Linear programming examples

There are several examples of linear programming intended to make the users of GIPALS familiar with it. These examples are included in GIPALS installation and can be found in ..\GIPALS\Examples folder.

Transport problem

Production (profit maximization) problem

Dietary optimization

Alloy mixture optimization

GIPALS Linear Programming $197.95 - 15000 Constraints & Variables | $297.00 - Unlimited Number of Constraints & Variables

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