Linear Regression
A registered nurse is trying to develop a diet plan for patients. The required nutritional elements are the total daily requirements of each nutritional element are as indicated in table 2:
The nurse has four basic types to use when planning the menus. The units of nutritional elements per unit of food type are shown in the table below. Note than the cost associated with a unit of ingredient also appears at the bottom of table 3.
Moreover, due to dietary restrictions, the following aspects should also be considered when the developing the diet plan:
The chicken food type should contribute at most 25% of the total calories intake that will result from the diet plan.
The vegetable food type should provide at least 30% of the minimum daily requirements for vitamins.
Provide a linear programming formulation for the above case. (No need to solve the problem.) Element | Milk | Chicken | Bread | Vegetables | Calories (X1) | 160 | 25% * 210 | 120 | 150 | Carbohydrates (X2) | 110 | 130 | 110 | 120 | Protein (X3) | 90 | 190 | 90 | 130 | Vitamins (X4) | 50 | 50 | 75 | 30% * 70 |
1. Define the objective
Meet the required daily nutritional allowance
2. Define the decision variables x1 = amount of calories x2 = amount of carbohydrates x3= amount of protein x4= amount of vitamins
3. Write the mathematical objective function Z = 2700 * x1 + 300 * x2 + 250 * x3 + 60 * x4
4. Write a one- or two-word description of each constraint
Allowed Calories
Allowed Carbohydrates
Allowed Protein
Allowed Vitamins
5. Write the right-hand side of each constraint
2700
300
250
60
6. Write <, =, or > for each constraint
≤ 2700
≥ 300
≥ 250
≥ 60
7. Write all the decision variables on the left-hand side of each constraint x1 x2 x3 x4 ≤ 2700 x1 x2 x3 x4 ≥ 300 x1 x2 x3 x4 ≥ 250 x1 x2 x3 x4 ≥ 60
8. Write the coefficient for each decision in each constraint
160 x1 + 110 x2 + 90 x3 + 50 x4 ≤ 2700
52.5 x1 + 130
The nurse has four basic types to use when planning the menus. The units of nutritional elements per unit of food type are shown in the table below. Note than the cost associated with a unit of ingredient also appears at the bottom of table 3.
Moreover, due to dietary restrictions, the following aspects should also be considered when the developing the diet plan:
The chicken food type should contribute at most 25% of the total calories intake that will result from the diet plan.
The vegetable food type should provide at least 30% of the minimum daily requirements for vitamins.
Provide a linear programming formulation for the above case. (No need to solve the problem.) Element | Milk | Chicken | Bread | Vegetables | Calories (X1) | 160 | 25% * 210 | 120 | 150 | Carbohydrates (X2) | 110 | 130 | 110 | 120 | Protein (X3) | 90 | 190 | 90 | 130 | Vitamins (X4) | 50 | 50 | 75 | 30% * 70 |
1. Define the objective
Meet the required daily nutritional allowance
2. Define the decision variables x1 = amount of calories x2 = amount of carbohydrates x3= amount of protein x4= amount of vitamins
3. Write the mathematical objective function Z = 2700 * x1 + 300 * x2 + 250 * x3 + 60 * x4
4. Write a one- or two-word description of each constraint
Allowed Calories
Allowed Carbohydrates
Allowed Protein
Allowed Vitamins
5. Write the right-hand side of each constraint
2700
300
250
60
6. Write <, =, or > for each constraint
≤ 2700
≥ 300
≥ 250
≥ 60
7. Write all the decision variables on the left-hand side of each constraint x1 x2 x3 x4 ≤ 2700 x1 x2 x3 x4 ≥ 300 x1 x2 x3 x4 ≥ 250 x1 x2 x3 x4 ≥ 60
8. Write the coefficient for each decision in each constraint
160 x1 + 110 x2 + 90 x3 + 50 x4 ≤ 2700
52.5 x1 + 130