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Breath takers, a health and fitness center, operates a morning fitness program for senior citizens. The program includes aerobic exercise, either swimming or step exercise, followed by a healthy breakfast in its dining room. The dietitian of Breath takers wants to develop a breakfast that will be high in calories, calcium, protein, and fiber, which are especially important to senior citizens, but low in fat and cholesterol. She also wants to minimize cost. She has selected the following possible food items, with individual nutrient contributions and cost from which to develop a standard breakfast menu.
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Choles- |
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Breakfast Food |
Calories |
Fat  (g) |
terol (mg) |
Iron  (mg) |
Calcium (mg) |
Protein (g) |
Fiber (g) |
Cost ($) |
|
1. Bran cereal (cup) |
90 |
0 |
0 |
6 |
20 |
3 |
5 |
0.18 |
|
2. Dry cereal (cup) |
110 |
2 |
0 |
4 |
48 |
4 |
2 |
0.22 |
|
3. Oatmeal (cup) |
100 |
2 |
0 |
2 |
12 |
5 |
3 |
0.10 |
|
4. Oat bran (cup) |
90 |
2 |
0 |
3 |
8 |
6 |
4 |
0.12 |
|
5. Egg |
75 |
5 |
270 |
1 |
30 |
7 |
0 |
0.10 |
|
6. Bacon (slice) |
35 |
3 |
8 |
0 |
0 |
2 |
0 |
0.09 |
|
7. Orange |
65 |
0 |
0 |
1 |
52 |
1 |
1 |
0.40 |
|
8. Milk-2% (cup) |
100 |
4 |
12 |
0 |
250 |
9 |
0 |
0.16 |
|
9. Orange juice |
120 |
0 |
0 |
0 |
3 |
1 |
0 |
0.50 |
|
(cup) |
 |
 |
 |
 |
 |
 |
 |
 |
|
10. Wheat toast |
65 |
1 |
0 |
1 |
26 |
3 |
3 |
0.07 |
|
(slice) |
 |
 |
 |
 |
 |
 |
 |
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The dietitian wants the breakfast to include at least 420 calories, 5 milligrams of iron, 400 milligrams of calcium, 20 grams of protein, and 12 grams of fiber. Furthermore, she wants to limit fat to no more than 20 grams and cholesterol to 30 milligrams. Formulate the linear programming model for this problem and solve.