Cody is planning a healthy fast food menu for a group of children for Pet Day at the elementary school. As a nutrition major, Cody want to plan a meal at the lowest possible cost from the McDonalds.
Here is the the pricing and nutrition information of the food that Cody can order for Pet Day.
|
Price |
|
Protein |
Fat |
Sodium |
> |
| Menu Item |
($) |
Calories |
(grams) |
(mg) |
> |
| Hamburger |
0.62 |
255 |
12 |
9 |
490 |
> |
| McLean Dlx |
1.79 |
320 |
22 |
10 |
670 |
> |
| Big Mac |
1.65 |
500 |
25 |
26 |
890 |
> |
| Small Fries |
0.68 |
220 |
3 |
12 |
110 |
> |
| McNuggets |
1.56 |
270 |
20 |
15 |
580 |
> |
| Honey |
0.00 |
45 |
0 |
0 |
0 |
> |
| Chef Salad |
2.99 |
170 |
17 |
9 |
400 |
> |
| Garden Salad |
1.96 |
50 |
4 |
2 |
70 |
> |
| Egg McMuffin |
1.36 |
280 |
18 |
11 |
710 |
> |
| Wheaties |
1.09 |
90 |
2 |
1 |
220 |
> |
| Yogurt Cone |
0.63 |
105 |
4 |
1 |
80 |
> |
| Milk |
0.56 |
110 |
9 |
2 |
130 |
> |
| Orange Juice |
0.88 |
80 |
1 |
0 |
0 |
> |
| Grapefruit juice |
0.68 |
80 |
1 |
0 |
0 |
> |
| Apple Juice |
0.68 |
90 |
0 |
0 |
5 |
> |
|
> |
|
|
|
|
|
|
|
| < |
|
Vit A |
Vit C |
Vit B1 |
Vit B2 |
Niacin |
Calcium |
Iron |
| < |
Menu Item |
% U.S. Recommended Daily Allowance (RDA) |
| < |
Hamburger |
4 |
4 |
20 |
10 |
20 |
10 |
15 |
| < |
McLean Dlx |
10 |
10 |
25 |
20 |
35 |
15 |
20 |
| < |
Big Mac |
6 |
2 |
30 |
25 |
35 |
25 |
20 |
| < |
Small Fries |
* |
15 |
10 |
* |
10 |
* |
2 |
| < |
McNuggets |
* |
* |
8 |
8 |
40 |
* |
6 |
| < |
Honey |
* |
* |
* |
* |
* |
* |
* |
| < |
Chef Salad |
100 |
35 |
20 |
15 |
20 |
15 |
8 |
| < |
Garden Salad |
90 |
35 |
6 |
6 |
2 |
4 |
8 |
| < |
Egg McMuffin |
10 |
* |
30 |
20 |
20 |
25 |
15 |
| < |
Wheaties |
20 |
20 |
20 |
20 |
20 |
2 |
20 |
| < |
Yogurt Cone |
2 |
* |
2 |
10 |
2 |
10 |
* |
| < |
Milk |
10 |
4 |
8 |
30 |
* |
30 |
* |
| < |
Orange Juice |
* |
120 |
10 |
* |
* |
* |
* |
| < |
Grapefruit juice |
* |
100 |
4 |
2 |
2 |
* |
* |
| < |
Apple Juice |
* |
2 |
2 |
* |
* |
* |
4 |
| < |
|
| < |
* Contains less than 2% of the U.S. RDA of these nutrients |
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Cody wants the meal to be nutritionally complete. The National Research Council publishes their Recommended Daily Allowances. In this publication, they contend that a diet (in this case the meal) should provide at least 100 percent of the U.S. RDA of numerous nutrients. The specific amount of the RDA depends on such factors as age, weight and gender. In addition, the council recommends daily sodium and cholesterol intakes be kept to at most 2.4 grams of sodium and 300 milligrams of cholesterol. Further, at most 30 percent of the calories consumed should come from fat, and at most 10 percent from saturated fat. Each gram of fat contains 9 calories.
Based on the above information, Cody wants to design a least-cost meal that provides at least 100% of the U.S. RDA of vitamins A, C, B1, B2, niacin, calcium, and iron; supplies at least 55 grams of protein; contains at most 3 grams of sodium; and contains at most 30 percent of its calories from fat. Only those foods list in the table above are available for the meal.
Formulate the LP model for Cody's problem. Develop a spreadsheet model of the problem and use Excel Solver to determine the least-cost meal that meets all the stated requirements.
What is the recommended meal? Is this meal reasonable? If not, modify the model to obtain what you believe to be a reasonable meal that meets the stated requirements.