Joyce and Marvin run a day care for preschoolers. They are trying to decide what to feed the children for lunches. They
would like to keep their costs down, but also need to meet the
nutritional requirements of the children. They have already
decided to go with peanut butter and jelly sandwiches, and some
combination of graham crackers, milk, and orange juice. The
nutritional content of each food choice and its cost are given in the
table below.
The nutritional requirements are as follows. Each child should
receive between 400 and 600 calories. No more than 30 percent of
the total calories should come from fat. Each child should consume
at least 60 milligrams (mg) of vitamin C and 12 grams (g) of protein. Furthermore, for practical reasons, each child needs exactly
2 slices of bread (to make the sandwich), at least twice as much
peanut butter as jelly, and at least 1 cup of liquid (milk and/or
juice).
Joyce and Marvin would like to select the food choices for each
child which minimize cost while meeting the above requirements.
(a) Formulate a linear programming model for this problem.
(b) Solve this model by the simplex method.