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The Diet Problem focuses on selecting food combinations to meet nutritional needs at minimal cost, often applied in meal planning for institutions. In the example provided, the optimal diet costs $7.90 and consists of 5 units of rice, 10 units of beans, and 2 units of chicken. This problem has applications in budget-constrained diets and humanitarian food distribution.

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11 views3 pages

OR Report

The Diet Problem focuses on selecting food combinations to meet nutritional needs at minimal cost, often applied in meal planning for institutions. In the example provided, the optimal diet costs $7.90 and consists of 5 units of rice, 10 units of beans, and 2 units of chicken. This problem has applications in budget-constrained diets and humanitarian food distribution.

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ireenaalamri
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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The Diet Problem in Operations Research

Problem Definition .1
The Diet Problem involves selecting a combination of foods to meet
nutritional requirements at the lowest possible cost. This problem is often
used to optimize meal plans in hospitals, schools, and food services while
.considering cost constraints

: Scenario
A person wants to plan their daily diet by choosing from three foods: rice,
beans, and chicken. Each food contains a certain amount of calories,
protein, and fat. The goal is to meet daily nutritional requirements while
.minimizing the cost
:Objective
.Minimize the total cost of the diet
:Nutritional Requirements
.At least 2,000 calories
.At least 50 grams of protein
.At most 70 grams of fat
: Food data
food $ Cost Calories Protein (g) Fat (g)
Rice unit/0.50$ 200 4 1
Beans unit/0.30$ 100 7 0.5
chicken unit/1.20$ 250 25 5
Problem Formulation/Modeling .2
:Decision Variables
:Let
.X1 : Number of units of rice
.X2 : Number of units of beans
.X3 : Number of units of chicken

:Objective Function
) Minimize the total cost (
Z=0.5 x 1+ 0.30 x 2 +1.20 x 3 Min

:Constraints
Calorie Requirement
200 x 1+100 x 2 +250 x 3 ≥ 2000

Protein Requirement
4 x1 +7 x 2 +25 x3 ≥ 50

Fat Limit
1 x1 +0.5 x 2 +5 x3 ≤ 70

Non-Negativity
x1 , x2 , x3 ≥ 0

: Optimal Solution ( using the Simplex Method ) .3


‫حل يدوي‬

Conclusion .4
:Summary
The Diet Problem optimizes food selection to meet
nutritional needs at the lowest cost. In the example, the
:optimal diet costs $7.90 and includes
.units of rice 5
.units of beans 10
.units of chicken 2
:Applications
.Meal planning in hospitals and schools
.Budget-constrained diets
.Humanitarian aid and food distribution

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