# The Learning Center runs a day camp for 6-10 year olds during the summer. Its manager, Elizabeth

## Question:

The Learning Center runs a day camp for 6-10 year olds during the summer. Its manager, Elizabeth Reed, is trying to reduce the center's operating costs to avoid having to raise the tuition fee. Elizabeth is currently planning what to feed the children for lunch. She would like to keep costs to a minimum, but also wants to make sure she is meeting the nutritional requirements of the children. She has already decided to go with peanut butter and jelly sandwiches, and some combination of apples, milk, and/ or cranberry juice. The nutritional content of each food choice and its cost are given in the table that accompanies this problem.
The nutritional requirements are as follows. Each child should receive between 300 and 500 calories, but no more than 30 percent of these calories should come from fat. Each child should receive at least 60 milligrams (mg) of vitamin C and at least 10 grams (g) of fiber.
To ensure tasty sandwiches, Elizabeth wants each child to have a minimum of 2 slices of bread, 1 tablespoon (tbsp) of peanut butter, and 1 tbsp of jelly, along with at least 1 cup of liquid (milk and/or cranberry juice).
Elizabeth would like to select the food choices that would minimize cost while meeting all these requirements.
a. Formulate and solve a linear programming model for this problem on a spreadsheet.
b. Formulate this same model algebraically?
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