# Linear Regression

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 x2 +...

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