The HeadStart runs a day camp for 6- to 10- year olds during thesummer. Its manager is trying to reduce the center's operatingcosts to avoid having to raise the tuition fee. The manager iscurrently planning what to feed the children for lunch. She wouldlike to keep costs to a minimum, but also wants to make sure she ismeeting the nutritional requirements of the children. She hasalready decided to go with peanut butter and jelly sandwiches, andsome combination of apples, milk, and/or cranberry juice. Thenutritional content of each food choice and its cost are given inthe table below:
| Bread | Peanut Butter | Jelly | | Milk | Juice |
| (slice) | (tbsp) | (tbsp) | Apples | (cup) | (cup) |
Unit Cost | $0.06 | $0.05 | $0.08 | $0.35 | $0.20 | $0.40 |
| | | | | | |
| | | Nutritional Data | | | |
Calories from Fat | 15 | 80 | 0 | 0 | 60 | 0 |
Calories | 80 | 100 | 70 | 90 | 120 | 110 |
Vitamin C (mg) | 0 | 0 | 4 | 6 | 2 | 80 |
Fiber (g) | 4 | 0 | 3 | 10 | 0 | 1 |
The nutritional requirements are as follow. Each child shouldreceive between 300 and 500 calories, but no more than 30% of thesecalories should come from fat. Each child should receive at least60 milligrams (mg) of vitamin C and at least 10 grams (g) offiber.
To ensure tasty sandwiches, the manager wants each child to havea minimum of 2 slices of bread, 1 tablespoon (tbsp) of peanutbutter, and 1 tbsp of jelly, along with at least 1 cup of liquid(milk and/or cranberry juice).
The manager would like to select the food choices that wouldminimize cost while meeting all these requirements.
Formulate and solve a linear programming model for this problemon a spreadsheet.
a) How many ounces of each type of food are included in oneserving of the lunch? (Round to three decimals)
| Bread | Peanut Butter | Jelly | Apples | Milk | Juice |
| (slice) | (tbsp) | (tbsp) | | (cup) | (cup) |
Diet (ounces) | | | | | | |
b) How many calories from fat are in one serving of the lunch?(Round to three decimals)
c) What is the total cost per serving of the lunch? (Round totwo decimals) $