Problem: 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:
Table: (Required Nutritional Element Total and Daily Requirements)
|
Calories
|
Not more than 2,700 calories
|
|
Carbohydrates
|
Not less than 300 grams
|
|
Protein
|
Not less than 250 grams
|
|
Vitamins
|
Not less than 60 units
|
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.
Table: (Required Nutritional Element and Units of Nutritional Elements Per Unit of Food Type)
|
Element
|
Milk
|
Chicken
|
Bread
|
Vegetables
|
|
Calories
|
160
|
210
|
120
|
150
|
|
Carbohydrates
|
110
|
130
|
110
|
120
|
|
Protein
|
90
|
190
|
90
|
130
|
|
Vitamins
|
50
|
50
|
75
|
70
|
|
Cost per unit
|
$0.42
|
$0.68
|
$0.32
|
$0.17
|
Moreover, due to dietary restrictions, the following aspects should also be considered when the developing the diet plan:
i) The chicken food type should contribute at most 25% of the total calories intake that will result from the diet plan.
ii) 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.