Problem 1 (Adapted from Hillier & Lieberman, 2005): 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 feed the children using food items 1,2, ..., n. One serving of food item i (i = 1,2,..., n) contains a total of C calories, of which fi are calories from fat, and pi grams of protein. In addition, each serving of food item i (i = 1, ..., n) costs bi dollars and contains Vij milligrams of vitamin j (j = 1, ...,10). 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 q; milligrams of vitamin j (j = 1, ...,10) and 12 grams of protein. Formulate a linear program to minimize the cost of meeting the nutritional requirements