Construct a diet linear programming using research using constraints and objective function and then find the solution using excel solver. MGMT511CaseI.pdf

MGMT 511 Quantitative Methods in Business

Spring 2023

Case Study I: Dieting Problem (10%, 3-4 person Group),

Due: March 18, 2023, @24:00

Upload your complete report in pdf format into MyGUST before the due date.

“Preparing the best possible meals at the least possible cost is the objective of food-systems management for

most feeding programs (e.g., hospitals, nursing homes, schools, and prisons). Menu planning is key since the

menu determines food, equipment, and personnel requirements. Menu planning, however, deceives both

nutrition experts and the public by appearing to be a simple procedure. The model must consider numerous

constraints. For example, the Food and Nutrition Board identified minimum intake levels for 29 nutrients (Often called recommended upper limits for fat, cholesterol, and sodium intake). All in all, it can get quite

complex to plan menus that meet all the nutritional constraints.

Nutrition cannot be the only goal, however. A simple diet model that meets the nutritional constraints at a

minimum cost can easily be developed, but nobody would eat the recommended diet. The diet is generally the

equivalent of the human-dog biscuit. One particular humorous story comes from the father of Linear

programming, George Dantzig. When George first created a personnel diet model in the early 1950s to help

him lose weight by controlling his diet, it recommended a bunch of weird stuff AND 500 gallons of vinegar. He eliminated vinegar as a possibility, and the next "optimal" diet included 200 bouillon cubes daily. When

he tried to drink 4 cubes dissolved in hot water for breakfast the next day, he had to spit the briny mixture out! After several more iterations of adding constraints and getting ridiculous recommendations, his wife

finally took over the diet.

Anyway, good diet models will include these additional constraints in terms of a separation rating or a

frequency constraint. Institutions that have implemented these menus have: (1) Realized 10 to 30% cost savings;

(2) Always met the nutrient constraints, which wasn't always the case before; (3) Actually had the same acceptance by the customers in terms of taste as those meals planned with

traditional methods.”1

Right after reading the text above, your group became aware of a humorous competition to be

held in Al Shaheed park two weeks later. The competition requires participants to have a well-

balanced diet, consuming food from well-known fast-food restaurants all day. The participant who

spends the minimum amount for the diet is selected as the winner at the end of the day. You

may select any fast food restaurants or have a portfolio of them for the items in your diet, such as

McDonald (https://www.mcdonalds.com/kw/en-kw/about-our-food/nutrition-calculator.html),

KFC (https://www.nutrition-charts.com/kfc-nutrition-facts-calorie-information), Burger King

(https://fastfoodnutrition.org/burger-king#google_vignette). Considering participating will be

fun, you identified one of your group members to join this activity. As a group, you support

your friend and help him/her to make the proper decision about the diet plan. After a short

discussion, you figured out the following tasks to be performed.

• Select a fast-food restaurant(s) to pick up menu items (at least 7-15) with nutrition

information.

• Search for a detailed nutrition analysis of a well-balanced daily diet for your

friend. You may get this information from the Internet sites such as

http://www.nal.usda.gov/fnic/foodcomp/. Sample information may include:

1 Eppen, G.D.,F.J. Gould, C.P. Schmidt (1998): Introductory Management Science, 5th Edition,

Prentice Hall.

According to a 1989 publication of the National Research Council of America

“nutritionally complete” means that a diet should provide the following nutrients: 1. Total Calories should be 2000 Calories or more

2. Carbohydrates should be 300 g or more

3. Dietary fiber should be 25 g or more

4. Total fat should be less than 65 g

5. Saturated fat should be less than 20 g 6. Cholesterol should be less than 300 mg

7. Sodium should be less than 2,400 mg 8. Furthermore, at most, 30% of the calories should come from fat, and at most,

10% should come from saturated fat.

• Address any personal preferences of your friend, such as being vegetarian, meat

lover, etc.

As soon as you collect the information above, you are very sure that you can formulate the

daily dieting menu problem as a minimum-cost linear programming model. However, you

should ensure that the recommended diet is eatable and acceptable to your friend regarding

his/her taste and preferences. In order to have an acceptable diet, you may add some

constraints into your formulation to enforce your preferences. E.g., having at least three drinks

daily, at most two soups daily, and so on. In order to get integer results, you may enforce the

decision variable to be integer using integer programming.

Case Study Deliverables:

A full fledge report with the following sections:

• Problem definition

• Data used in the case with appropriate references.

• Your clear description of the LP model

• Lingo or Excel formulation and solution of the model

• Clear suggestion to your friend. E.g., daily menu (breakfast, lunch, dinner), the

total cost of the menu, its suitability to his/her preferences, etc.

• Conclusion

• Appendix (Lingo/Excel model and solution)