Dallas Stars hockey team wants to hire a dietitian in order to develop new meal plans for its players during the next NHL season. The dietitian responsibility is to attempt to determine a nutritious menu for the team. The team managers and coaches have set the following nutritional guidelines for each serving: Between 1,500 and 2,000 calories At least 20 but no more than 60 g of fat At least 40 g of carbohydrates At least 30 g of protein At least 5 mg of iron No more than 30 mg of cholesterol The dietitian needs to select the menu from seven basic food items, as follows, with the nutritional contribution per pound and the cost as given: Calories (per lb.) Iron (mg/lb.) Protein (g/lb.) Carbohydrate (g/lb.) Fat (g/lb.) Cholesterol (mg/lb.) Cost ($/lb.) Chicken 520 4.4 17 0 30 180 0.8 Fish 500 3.3 85 0 5 90 3.7 Ground beef 860 0.3 82 0 75 350 2.3 Dried beans 600 3.4 10 30 3 0 0.9 Lettuce 50 0.5 6 0 0 0 0.75 Potatoes 460 2.2 10 70 0 0 0.4 Milk (2%) 240 0.2 16 22 10 20 0.83 The management wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving. Formulate a linear programming model for this problem (The mathematical model can be either typed or handwritten. Do not put the mathematical model inside the excel file). Solve the model by using the computer (Please submit the excel file containing the solution and the solver configuration along with the report) and report the optimal solution and objective function in your report. If a serving of each of the food items (other than milk) was limited to no more than a half-pound, what effect would this have on the solution? (Justify your answer)
Dallas Stars hockey team wants to hire a dietitian in order to develop new meal plans for its players during the next NHL season. The dietitian responsibility is to attempt to determine a nutritious menu for the team. The team managers and coaches have set the following nutritional guidelines for each serving:
- Between 1,500 and 2,000 calories
- At least 20 but no more than 60 g of fat
- At least 40 g of carbohydrates
- At least 30 g of protein
- At least 5 mg of iron
- No more than 30 mg of cholesterol
The dietitian needs to select the menu from seven basic food items, as follows, with the nutritional contribution per pound and the cost as given:
|
|
Calories (per lb.) |
Iron (mg/lb.) |
Protein (g/lb.) |
Carbohydrate (g/lb.) |
Fat (g/lb.) |
Cholesterol (mg/lb.) |
Cost ($/lb.) |
|
Chicken |
520 |
4.4 |
17 |
0 |
30 |
180 |
0.8 |
|
Fish |
500 |
3.3 |
85 |
0 |
5 |
90 |
3.7 |
|
Ground beef |
860 |
0.3 |
82 |
0 |
75 |
350 |
2.3 |
|
Dried beans |
600 |
3.4 |
10 |
30 |
3 |
0 |
0.9 |
|
Lettuce |
50 |
0.5 |
6 |
0 |
0 |
0 |
0.75 |
|
Potatoes |
460 |
2.2 |
10 |
70 |
0 |
0 |
0.4 |
|
Milk (2%) |
240 |
0.2 |
16 |
22 |
10 |
20 |
0.83 |
The management wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving.
- Formulate a linear programming model for this problem (The mathematical model can be either typed or handwritten. Do not put the mathematical model inside the excel file).
- Solve the model by using the computer (Please submit the excel file containing the solution and the solver configuration along with the report) and report the optimal solution and objective function in your report.
- If a serving of each of the food items (other than milk) was limited to no more than a half-pound, what effect would this have on the solution? (Justify your answer)
The linear programming method is used to determine a maximum or minimum value for a mathematical model while taking into account the linear relationships which represent the model's requirements generally known as constraints.
Taking the following variables for the respective serving –
C - Chicken
F - Fish,
G - Ground Beef
D - Dried Beans
L – Lettuce
P - Potatoes
M - Milk (2%).
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