# 10.6.3. Linear Programing and Optimization

Two packages of food supplies are available; the first gives 4 calories and has 6 units of vitamin C, and the second gives 3 calories and has 4 units of vitamin C. We need at least 37 calories and 22 units of vitamin C. Given that the prices of the first and the second are LE and LE respectively, state the objective function used to determine the minimum cost of buying the needed nutrients.

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### Example

Two packages of food supplies are available; the first gives 4 calories and has 6 units of vitamin C, and the second gives 3 calories and has 4 units of vitamin C. We need at least 37 calories and 22 units of vitamin C. Given that the prices of the first and the second are LE and LE respectively, state the objective function used to determine the minimum cost of buying the needed nutrients.

### Solution

Suppose is the number of the first type of package of food supplies, and is the number of the second type. Since the price of one of the packages of the first type is LE, the total price of all of these types of packages is LE, and since the price of one of the packages of the second type is LE, the total price of all of these types of packages is LE. Therefore, if the total price of all the packages is , the objective function is . The other information given in the question helps to determine the feasibility region, but it is not needed to determine the objective function.

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