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¢, each scoop of chocolate ice cream costs 20¢, each bottle of cola costs 30¢ and each piece of pineapple cheesecake costs 80¢. 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.