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    Linear programming problem formulation

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    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:

    Table 2
    (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 3
    (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.

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    This posting contains a formulation to following LPP.