We designed a model that would take input of a person's specifications, and then based on that would give a meal plan for the person for a week; great for busy people to stay healthy as well.

1. Group 6 Jin, Kevyani, Seeburger, Singhi,
Stroin
Diet Problem
Brief Case Description:
Eating a balanced diet is vital for good health and wellbeing. Food provides our bodies with the energy, protein,
essential fats, vitamins and minerals to live, grow and function properly. With multiple things going on, it can be
extremely hard to keep track of nutrition intake, not to mention, the biggest problem for a college student is to
live on a strict, and sometimes very tight budget.
Factors considered for this analysis includes a Drexel student, non-vegetarian, male ranging from age 19-23,
with a weight range of 160-170 lbs., height range between 66-72 inches and BMI (Body Mass Index) between
18.5-24.9 (normal weight). This study analyzes the best possible scenario and create a model for 1 day to meet
the daily average nutrient intake while constricting spending to a pre-set price ceiling, by using linear models in
Excel.
Inputs:
• Height
• Weight
• Gender
• Age
• Activity level (1-4)
Goal: Minimize Cost; buy amt
Data Gathered:
• Calories
• Vitamins
• Fat
• Carbohydrates
• Protein
• Cost of ingredients (gathered from local Fresh Grocer)
Basic Model with Solution:
4-5 Variables for 1 day
Data sources:
Fresh Grocer website, MyFitnessPal, https://www.nutritionvalue.org/, https://www.nutrition.gov/,
https://ndb.nal.usda.gov/ndb/search/list, https://www.medicalnewstoday.com/articles/245588.php

2. Group 6 Jin, Kevyani, Seeburger, Singhi,
Stroin

3. The Diet Problem
Group 6
Pedram Keyvani
Hongyi Jin
Colin Stroin
Robie Seeberger

4. Determining the Least Expensive and Healthiest Food
Purchase/Consumption Plan
Case Description
Drexel University hosts the Nutrition Education Program as an outlet for
nutritional information to reach Philadelphia public-school students. The Program along
with the Drexel University nutrition department, both hope to develop a way for students
in public schools as well as in Drexel University to obtain a personalized meal plan. The
college students as well as the public-school students have extremely small budgets for
food and very limited knowledge of nutrition. The students also often have amateur
cooking skills meaning they have experience only with very simple and common meals.
The team was asked to create an interactive model to help students craft their own
meals at an affordable price, all while satisfying official nutrition requirements. More
specifically, the team looks to understand the quantity of groceries a Drexel student or
public-school student should buy weekly to minimize cost, as well as achieving the
healthiest dietary balance possible. The case is inspired by the recognized need for
eating a balanced diet while achieving a healthy lifestyle. It is recognized as extremely
important that students specifically, meet or exceed the necessary dietary guidelines in
order to perform at the highest cognitive level in classes and at peak physical capability.
Most college students struggle with diet problems because they lack time or money to
ensure sufficient intake of protein, essential fats, vitamins, and minerals. However, a
healthy balance of these nutrients can be achieved and approximated for lowest cost.
Managerial Report

5. Diet planning aims at achieving the low possibility of inadequacy and still manage
to reach the UL (Tolerable Upper Intake Levels) for each of the required nutrients.
However, most people have neither the money nor the time to watch out for what they
eat. It is not uncommon to find people relying on their appetite and aesthetic-driven
desires to determine the constituents of their daily meals. This research set out to
explore the issue of dietary planning and hence recommend an Adequate Intake (AI).
The recommendation will aid individuals in deciding the right meals that fit recommend
dietary requirements.
Additionally, the development of essential values with regard to nutrient content
in each meal needed a mathematical solution. In the long run, the group required a
linear objective function to distinguish the relationship between the gathered nutritional
information (%), prices, and the desired outcomes (amount buy/consume) to minimize
cost.
To compensate for a flexible model that adjusts for different users, the group
structured an input section linked back to the data and our mathematical model, within
excel. This not only strengthens our model, but also helps to constrain our data
according to the user. For example, our inputs consist of characteristics such as,
weight, height, activity, level, age, and gender. Since we are working with the biological
human body in order to give the best nutrition possible, it is necessary to have a flexible
model as such, or else our results would not be reliable at all. In this day and age, the
importance of custom treatments is evident in the world of medicine; thus, the group is
glad to have achieved such goal with the model.

6. First, the group required a function that would be used successfully in the
optimization of known variables. Once there was a balance and an established trend
under an unbiased and accurate function, the data would be expressed as patterns of
the model’s characteristics. The group needed inspiration from optimization theories
such as duality, convexity, decomposition, and the generalization of such theories. After
choosing the correct desired quantities, the group needed to find a feasible solution
despite the inconsistency of the diet and cost constraints.
Our optimal solution shows the best foods to be purchased/consumed with a cost
minimizing objective. As shown in the graph below, the cost is kept at the low of $14 per
day (for a week). The model strived to take into account a well diverse diet throughout
the week. This the group analyzed the best combination of ingredients to fulfill the
essential nutritional needs.
Meats
Beef Chicken Breast Turkey Salmon
Carbs
Rice Whole Grain Bread Pasta Cereal
Fig 1
The group set its prices from the most popular grocery store around campus,
Fresh Grocer. The group analyzed the prices of each food available at store and
optimized it in a way that packaged goods that can’t be purchased per ounce end up
reflecting our price objective the right way. In other words if we were to set actual prices
of an item such as cereal with nutritional facts being per serving we would get a very

7. high cost at the end of the week to fulfil those nutrients, and that is what the group
released; therefore, prices were adjusted with the daily intake values to get the realistic
cost minimization.
Key Considerations
The specific data required for the experiment included the subject’s dietary
subscription (vegetarian or otherwise), sex, weight, height, and body mass index. In this
setup, a male student was chosen. The age of choice was a range between 19 and 23
and a height of 66-72 inches. For body mass index, the group chose 18.5-24.9 because
it represents most people having normal weight.
Gender plays a crucial role in the nutritional needs of a person, and hence the
specifications for this experiment were strictly considerate of such requirements. A
perfect example to demonstrate the case for gender and dietary requirements is the
nutritional difference between calories requirements by men and women. The human
body requires calories so that muscle energy can be generated. The difference
emerges when the study subject has less or more muscles than the average person.
This difference is evident for men and women seeing that men have more masculine
bodies than women. Other nutrients that are differently recommended for both genders
include vitamins. Vitamins needs for women are higher than those of men. Similarly,
women trying to get pregnant or those that are pregnant have higher foliate needs than
men. The same case applies for the mineral rundown, whereby women are considered
to have more mineral needs than men owing to menstrual cycles.
Moreover, the group realized the risk of vitamin overdose that could be very
dangerous to consumers. Therefore, we set a max intake level per week for Iron,

8. Vitamins A, B-12, etc. Based on the research overdose on Iron is especially risky and
could lead to even death. Other vitamin overdose can also lead to long-term health
issues within the organs.
The Body Mass Index (BMI) quantifies the amount of tissue mass. This mass
includes bone, muscle, and fat. Hence, the BMI categorizes people as either normal
weight, overweight, or underweight. Additionally, a person may be classified as obese if
their weight exceeds the limits of the overweight indicator in the BMI. The Body Mass
Index (BMI) affects the number of nutrients that a person should have in a single day.
For example, an underweight person has fewer muscles than an average person. As
such, they require less energy and hence it is recommendable to have lower calories
intake than those of average people. On the other hand, an overweight person may
have a more muscular body pattern in comparison to the average person. This
knowledge makes the investigation more reliable and applicable since it references the
Body Mass Index (BMI) of an average person. As such, the figures recommended from
experimental data can easily be applied to persons in different Body Mass Index (BMI)
categories with obvious changes.
When a person abstains from meat intake, their dietary concerns are much
different than those of an average person. In general, a vegetarian would register more
calcium deficiencies than the average person owing to the intake of vegetables that
have less calcium content than dairy foods. Dairy foods are the biggest source of
calcium, yet some vegetarians avoid daily product as a lifestyle or dietary choice. For
such reasons, intake of vegetables such as broccoli or bok choy may not sufficiently
substitute the calcium needs of the body. For the experiment, this presents a level of

9. bias and complexities in prediction because the data would not account for a holistic
approach to the nutrient value of food. Other foods that may have shown similar
disadvantages to the researcher include iron, iodine, protein, and Vitamin B12. In this
regard, a non-vegetarian person was chosen.
Nutritional principles may be uniform throughout a person’s life, but still, various
phases of life require special dietary patterns. This experiment chose a young adult. At
this point in the person’s life, the body still has the chance to make new bones.
Additionally, the hormonal composition of their bodies allows for the building of muscles.
Basically, the range chosen for age is appropriate because it represents a stage that
sets up the body structure and dietary characteristics for the rest of a person’s life. The
experiment also took note of the need for a person’s in this age bracket to take certain
nutrients such as calcium, iron, and proteins. Additionally, a person in their 20s has
slowed metabolisms. The person cannot eat as heavily as they used to when they were
teenagers, or else their health may deteriorate.
Another factor considered when choosing age is the issue of a person’s lifestyle.
In the early twenties, a person may be in college or freshly graduated. Their lives are
characterized by limited freedom in terms of finance and schedules. The lack of
financial freedom was the basis on which this experiment was founded. On the other
hand, the issue of time is all about knowledge requirements which, for various reasons,
remains a major gap as far as dietary studies are concerned.
Thorough Description of Work Done
The experiment involved collection of data from food taken by the subject.
Attention was on specific nutrients including Calories, Vitamins, Fat, Carbohydrates,

10. and Protein. The percentage of the foods was recorded for every meal that the subject
had. Additionally, the cost of these meals was recorded. However, the meals also
contained other nutrients which the experiment also accounted for because they
contributed directly to the second variable, the cost. About 4-5 variables were
accounted for in one day, and the recorded information was availed for analysis. All the
data required about cost was gathered from the local diner.
The linear programming approach was crucial in getting the desired effect and
meeting the goals of the experiment. First, the decision variables were identified. These
variables include the percentages of various nutrients present in the meals taken by the
subject and the cost of the meals. The second step involved the formulation of the
objective function. An objective function, in this case, would aid in the prediction of
various variables by establishing a link between experimental variables. The function is
obtained through graphical methods. By plotting a graph of the cost of the whole meal
with the inclusion of other nutrients against percentages of the specific nutrient, a plot is
obtained. While the plot may fail to provide a perfect linear outcome, a linear model may
provide a line of best fit. Therefore, the points on the graph gave a linear relationship
that essentially made them relatable.
From the established linear model, the function of the model may be used for
prediction of subsequent values. The experimental data can be used to formulate
various constraints when it is related to the linear model from the above procedure. For
various desired percentages (700 percent for Vitamin A, Vitamin C, Vitamin B12,
Vitamin D, Proteins, Carbohydrates, calcium, and fats, 311 for iron, 64 oz for water, and
2207.838 units for calories).

12. The Ideal
Dietary
Supply
Forecast
Per Week
Pedram, Robie, Colin, Hongyi

13. Case
 Drexel University Nutrition
Education Program
 Drexel University Nutrition
Department
 Minimize cost
 Maintain optimal dietary
balance

14. Background
 Diet and its possible negative
impact on Health:
 Obesity
 Heart Disease
 Diabetes
 Cancer
 High Blood Pressure

16. Problem Statement
 A Drexel student who is busy and still needs to maintain
a healthy diet. The student needs to figure out what to
buy each week from the fresh grocer nearby that also
minimizes cost.

17. Approach
 Design a linear model
 Minimize costs
 Daily intake of essential nutrients.
 Utilize Excel Solver
 Sources: USDA Website
Fresh Grocer
Netrition.com

18. Data (shortened)

19. Constraints

20. Results

21. Inputs for customization purposes
 Weight
 Height
 Gender
 Activity
 Age

23. Challenge
 Gather the right data
 Turning units into usable amounts
 Think through inputs

24. Possible meals
 Breakfast:
 Bread, cheese, honey, milk, cereal, French toast, tea,
omelet
 Lunch:
 Pasta and chicken, Spaghetti Bolognaise, rice and
meat stew, soup, grilled salmon
 Snacks: Fruit, nuts, yogurt
 Dinner: Steamed vegetable and rice, chicken
sandwich, Burger with lettuce and tomato

25. Improvements looking ahead
 Increase nutrients
 Increase food choices
 Add meal out puts (Monday-
Sunday)

26. Questions?

27. Age (years) 25 Code
Height (cm) 180 1
Weight (kg)
60 2
Activity (1-5)
2 3
Gender (M or F) M 4
5
in to cm
Inches to cm 70 --> 177.80
lbs to kg
Pound to kg 160 --> 72.57
Reference
Inputs
http://www.calculator.net/calorie-calculator.html
Activity Lev

28. Activity Levels Description
Sedentary little or no excercise
Lightly Active
excercise/sports 1-3 times per
week
Moderately
Active
excercise/sports 3-5 times per
week
Very Active
hard excercise/sports 6-7 times per
week
Extra Active
very hard excercise/sports or
physical job
Activity Levels reference

29. https://shop.t
hefreshgrocer
.com/store/e7
e1123699/pro
duct/0020050
1000008
https://shop.thefreshgro
cer.com/store/e7e11236
99/product/0020456000
0009
https://shop.thefr
eshgrocer.com/sto
re/e7e1123699/pr
oduct/0002265571
5610
https://sh
op.thefres
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m/store/e
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9/product/
00208200
000008
Meal Beef (4oz)
Chicken breast (4oz)
price(lb)
Turkey (4oz)
Salmon
(5oz)
Brand
Fresh Ground
Beef
Fresh Chicken Breast
Butterball Ground
Turkey
Fresh
Salmon
Cost $1.02 $2.09 $0.75 $2.50
A 0% 0.48% 1% 8%
C 0% 0% 0% 10%
B-12 40% 6.3% 17% 76%
D 0.75% 1.50% 3% 156%
Protein 39% 69% 32% 20%
Calories 348 187 170 240
Carbohydrates 0% 0% 0% 0%
Iron 12% 6% 6% 3%
Calcium 2% 1.7% 2% 0%
Fat 35% 6.15% 11% 5.83%
Number of servings
Max # servings allowed 12.00 12.00 12.00 10.00
Consume Amount
Buy amount 7.541244244 7.999985329 3.946617956 2.2301676
Cost $7.71 $4.18 $2.95 $5.57
Objective min cost $98.05
Constraints: max actual
vitamin A 3500% >= 1095% >=
vitamin C >= 1752% >=
B-12 2000% >= 925% >=
D 2000% >= 700% >=
Protein 2100% >= 1850% >=
Carbohydrates 1400% >= 1031% >=
Iron 1311% >= 581% >=
Calcium 1000% >= 700% >=
Fat 900% >= 700% >=
Meats

30. Calories >= 15464.70696 >=
Fruits are integers
https://www.netrition.com/rdi_page.html daily values
https://ods.od.nih.gov/factsheets/Iron-HealthProfessional/
https://ndb.nal.usda.gov/ndb/foods/show/2871?manu=&fgcd=&ds=

31. https://shop.thefres
hgrocer.com/store/
e7e1123699/produc
t/00041190008926
https://shop.thefres
hgrocer.com/store/
e7e1123699/produc
t/00073410000267
https://shop.t
hefreshgrocer
.com/store/e
7e1123699/p
roduct/00073
410000267
https://shop.thefr
eshgrocer.com/sto
re/e7e1123699/pr
oduct/0001862770
3105
https://sh
op.thefres
hgrocer.co
m/store/e
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9/product/
00041190
037766
https://sh
op.thefres
hgrocer.co
m/store/e
7e112369
9/product/
00000000
047272
https://sh
op.thefres
hgrocer.co
m/store/e
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9/product/
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271224
Rice (.25 cup)
price(32oz)
Whole Grain Bread
(1 slice) price(16)
Pasta (3oz)
price(9oz.)
Cereal (1 cup)
price(9cups)
Carrots (oz
)
Potato
(150g)
Kale (5oz)
ShopRite Rice -
Long Grain Enriched
Arnold Buitoni
Kashi 7 Whole
Grain Puffs Cereal
Potato-
Yellow
Fresh
Express
$1.59 $4.49 $2.75 $3.49 $0.06 $0.99 $3.49
0% 0% 0% 0% 94.00% 0% 31%
0% 0% 0% 0% 3.00% 29% 17%
0% 0% 0% 0% 0.00% 0.00% 0.00%
0% 0% 0% 0% 0.00% 0.00% 0.00%
6% 5% 6% 4% 1% 8% 0%
160 120 240 70 52 116 50
12% 7% 15% 5% 9% 6% 3%
8.00% 8% 6% 2% 4.00% 27% 15%
0% 4% 2% 0% 0.90% 5% 15%
0% 3% 3% 0% 0% 0% 1%
14.00 16.00 6.00 7.00 12.00 12.00 7.00
5.682598801 5.179463756 6 0 2.0489069 2.118984 0.3708695
$1.59 $4.49 $5.50 $0.00 $0.13 $2.10 $1.29
min
700%
700%
700%
700%
700%
700%
311%
700%
700%
Carbs V

32. 15454.866

33. https://shop.th
efreshgrocer.co
m/store/e7e11
23699/product/
000712792611
26
https://sh
op.thefres
hgrocer.co
m/store/e
7e112369
9/product/
00014500
004208
https://shop.thefres
hgrocer.com/store/
e7e1123699/produc
t/00014500004130
https://shop.t
hefreshgrocer.
com/store/e7
e1123699/pro
duct/0004119
0049769
https://shop.thefreshgr
ocer.com/store/e7e112
3699/product/00052159
012021
Lettuce (3oz)
price (9oz)
Onion
(2/3cup)
Broccoli (1 cup)
White
Mushroom (8
oz)
Skim Milk (1 cup)
price(64 fl oz)
Water
Fresh Express Birds Eye Birds Eye Shop Rite Stonyfield Tap
$3.29 $0.62 $0.32 $2.00 $4.79 $0.00
14% 0% 0% 0 10% 0%
30% 0% 50% 0 0% 0%
0.00% 0.00% 0.00% 1.50% 0% 0%
0.00% 0.00% 0.00% 4.00% 25% 0%
0% 0% 0% 44% 14% 0%
15 30 30 15 80 0
1% 2% 1% 47% 4% 0%
4% 0% 0% 0% 0% 0%
2% 0% 2% 0% 30% 0%
0% 0% 0% 9% 0.00% 0%
14.00 15.00 15.00 14.00 16.00 -
0.948909656 0.5333375 1.1504485 0 11.16135734 0
$3.29 $0.33 $0.37 $0.00 $9.58 $0.00
Iron mg
Men 8 44.44%
Women 18 100.00%
Vegies Beverages

35. https://sh
op.thefres
hgrocer.co
m/store/e
7e112369
9/product/
00613008
715267
https://shop.the
freshgrocer.com
/store/e7e1123
699/product/00
000000031516
https://shop.the
freshgrocer.com
/store/e7e11236
99/product/000
00000031073
https://www.thefres
hgrocer.com/pd/App
les/Red-Delicious/1-
oz/000000040150/
https://shop.thef
reshgrocer.com/s
tore/04af123782
/product/000000
00040112
https://shop.thefreshg
rocer.com/store/04af1
23782/product/00000
000098458
Tea Tomato (6 oz)
Orange (per
fruit)
Apple Banana Strawberries
Arizona
Green Tea
Fresh Tomatoes -
Vine Ripe
Fresh Navel
Oranges
Apples Red Delicious Fresh Bananas Fresh Strawberries
$0.99 0.93$ 1.00$ 0.74$ 0.04$ $0.22
0% 28% 6% 1% 52% 0%
25% 39% 116% 8% 17% 160%
0% 0.00% 0% 0% 0% 0%
0% 0.00% 0% 0% 0% 0%
0% 2% 2% 0% 2% 2%
70 22 62 72 22 45
0% 2.2 5% 6.3% 1.66% 4%
0% 3% 1% 1% 0% 4%
0% 2% 5% 1% 0% 2%
0% 0 0 7% 0% 0%
14.00 7.00 7.00 7.00 7.00 7.00
2.4085146 2.240697031 3 2 0 2
$2.97 $2.08 $3.00 $1.48 $0.00 $0.44
ages Fruits (1 item medium size)

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ocer.com/store/04af123
782/product/00000000
034210
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r.com/store/04af123782/p
roduct/00073420516208
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04af123782/produc
t/00041190034154
https://shop.thef
reshgrocer.com/s
tore/04af123782
/product/000290
00016699
Watermelon (24oz)
price(6lbs)
Cottage cheese (4oz)
price(16 oz)
Honey (1tbsp)
price(12 oz)
Nut Mix (1oz)
price(10.3)
Fresh Watermelon Daisy ShopRite
Planters
Nutrition
5.99$ $3.19 $3.49 4.99$
77% 4% 0% 0%
92% 0% 2.03% 0%
0% 32% 0.00% 0%
0% 2% 0.00% 0%
8% 28% 0% 12%
207 90 60 170
17% 1% 6% 2%
9% 0% 7.91% 8%
5% 8% 2.03% 4%
2% 4% 0% 23%
8.00 7.00 12.00 30.00
7.993711389 4.88316389 2.563620665 9.503330009
$11.98 $6.38 $3.49 $4.99
Other

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rocer.com/store/04af1
23782/product/000411
90450015
https://sh
op.thefres
hgrocer.co
m/store/0
4af123782
/product/0
00254840
00131
eggs (1 Large egg)
Price(dozen)
Tofu
Yogurt (1 pack)
Price (4 pack)
ShopRite Large White
Eggs
Nasoya Activia
3.19$ 2.99$ $2.99
6% 0% 0%
0% 0% 0%
10% 0% 21%
11% 0% 0%
12% 8% 24%
70 45 140
0% 1% 7%
4% 4% 0%
2% 6% 15%
8% 3% 0%
28.00 5.00 8.00
3.072529744 2.8018146 7.116278218
$3.19 $2.99 $5.98
Other