Diet Problem
My diet requires that all the food I eat come
from one of the four "basic food groups" (chocolate cake, ice cream,
soda and cheesecake). At present, the following four foods are
available for consumption: brownies, chocolate ice cream, cola and
pineapple cheesecake. Each brownie costs 50 cents, each scoop of chocolate
ice cream costs 20 cents, each bottle of cola costs 30 cents and each piece of
pineapple cheesecake costs 80 cents. Each day, I must ingest at least 500
calories, 6 oz of chocolate, 10 oz of sugar and 8 oz of fat. The
nutritional content per unit of each food is:
| |
Calories |
Chocolate (ounces) |
Sugar (ounces) |
Fat (ounces) |
| Brownie |
400 |
3 |
2 |
2 |
| Chocolate ice cream (1 scoop) |
200 |
2 |
2 |
4 |
| Cola (1 bottle) |
150 |
0 |
4 |
1 |
| Pineapple cheesecake (1 piece) |
500 |
0 |
4 |
5 |
Formulate a linear programming model that can be used to satisfy my daily nutritional requirements at
minimum cost.