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## Super Size

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### ... to eat 2500 calories a day, so we would actually expect Spurlock to lose weight ... figure in our simulation to determine best- and worst-case scenarios. ... – PowerPoint PPT presentation

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Title: Super Size

1
Super Size
e
An Optimization Problem
• MME 2007

2
Background
• In 2003, documentary film-maker Morgan Spurlock
set out to expose the fast food industrys role
in Americas obesity epidemic.

3
Background
• For thirty consecutive days, Spurlock ate nothing
but McDonalds food anything offered on the menu
was fair game.

4
Background
• He had three rules for his experiment

5
Background
• He had three rules for his experiment
• He would eat exclusively from the McDonalds menu

6
Background
• He had three rules for his experiment
• He would eat exclusively from the McDonalds menu

2. He would super size his meal whenever an
7
Background
• He had three rules for his experiment
• He would eat exclusively from the McDonalds menu

2. He would super size his meal whenever an
3. He would try everything on the menu at least
once.
8
Background
• The results were not pretty

9
Background
• The results were not pretty
• Spurlock gained about 25 pounds over the
month-long experiment,

10
Background
• The results were not pretty
• Spurlock gained about 25 pounds over the
month-long experiment,
• And he suffered from various health problems such
as chest pains, shortness of breath, and liver
trouble.

11
What does this have to do with math?
• We are interested in whether or not Spurlock
could have designed his experiment more
intelligently.
• Simply put, could Spurlock go on an
all-McDonalds diet for thirty days without
causing such harm to his health?

12
What does this have to do with math?
• This is where optimization comes into play
• We want to design an optimal menu for Spurlock.
• But how should we define optimal?

13
McStrategy
• In this case, we will define an optimal menu as
one that meets these criteria

14
McStrategy
• In this case, we will define an optimal menu as
one that meets these criteria
• The menu consists only of food served at
McDonalds restaurants.

15
McStrategy
• In this case, we will define an optimal menu as
one that meets these criteria

2. Spurlock super sizes his meal when asked.
16
McStrategy
• In this case, we will define an optimal menu as
one that meets these criteria

3. Specific nutritional requirements are met,
namely the RDI of vitamins A and C, calcium,
iron, protein, carbohydrates, fat, and fiber.
For our purposes, these values will be based on
Spurlocks needs, taking into account his sex,
age, height, and weight.
17
McStrategy
• In this case, we will define an optimal menu as
one that meets these criteria

4. Spurlocks daily caloric intake is minimized.
18
McStrategy
• We also need some simplifying assumptions
• We will only consider one day in the experiment,
as each days nutritional and caloric
requirements are independent of the others. We
can later scale this one-day simulation to
approximate a 30-day experiment.

19
McStrategy
• We also need some simplifying assumptions
• We will consider only non-negative integral
values for the amount of each menu item eaten.

20
McStrategy
• We also need some simplifying assumptions
• We will assume that Spurlock will not mind eating
the same thing every day.

21
McStrategy
• We also need some simplifying assumptions
• We will exclude Spurlocks rule that each item
available on the menu must be eaten at least once
over the course of the month. (Remember, we are
only looking at one day of the experiment.)

22
A First Helping The Basic Model
• The first model we consider is an integer
programming model.

23
A First Helping The Basic Model
• We have 136 decision variables (the number of

24
A First Helping The Basic Model
• If we let xi represent the number of item i eaten
(1 i 136), then our objective function is

25
A First Helping The Basic Model
• If we let xi represent the number of item i eaten
(1 i 136), then our objective function is
• Minimize
• Where ci is the number of calories of item i.

26
A First Helping The Basic Model
• Our objective function is subject to our
pre-specified nutritional constraints

27
A First Helping The Basic Model
• Nutritional Constraints

(Vitamin A, Vitamin C, Calcium, Iron, protein,
fat, carbohydrates, and dietary fiber.)
28
A First Helping The Basic Model
• We also specify the implicit constraint that the
amount of each menu item ordered (and eaten) be a
non-negative integer
• xi 0, xi integer

29
A First Helping The Basic Model
• We can set up this integer programming model in a
spreadsheet program (were using gnumeric) and
use the built-in Solver function to specify our
constraints.

30
A First Helping The Basic Model
• We can set up this integer programming model in a
spreadsheet program (were using gnumeric) and
use the built-in Solver function to specify our
constraints.
• When we run this model, we obtain a menu in which
Spurlock consumes a total of 1795 calories each
day.
• Spurlocks nutritionist advised him to eat 2500
calories a day, so we would actually expect
Spurlock to lose weight (about 6 pounds) with

31
A First Helping The Basic Model
• A six-pound weight loss is a good thing, right?
Welllets look at the actual menu.

32
A First Helping The Basic Model
• This model generated the following daily menu for
Spurlock

1 Ketchup packet 2 Caesar salads with grilled
chicken 45 side salads 46 half-and-half creamer
packets
33
Going Back for Seconds Binary Model
34
Going Back for Seconds Binary Model
• Due to the unrealistic nature of our previous
results, we adopt a new constraint for our model.

35
Going Back for Seconds Binary Model
• Due to the unrealistic nature of our previous
results, we adopt a new constraint for our model.
• We will limit Spurlock to eating no more than 1
of each menu item during the day.
• So each xi0 or xi1.

36
Going Back for Seconds Binary Model
• This new constraint will hopefully yield a more

37
Going Back for Seconds Binary Model
• When we run the revised model, we see that
Spurlocks daily caloric intake has increased to
2820 calories also, his daily fat intake is at
118.5 grams.

38
Going Back for Seconds Binary Model

1 Quarter Pounder 1 California Cobb salad 1
Small French Fries 1 side salad 1 Medium French
Fries 1 English muffin 1 Large French Fries 1
order of hash browns 1 Hot Mustard Sauce 1
packet of peanuts 1 Tangy Honey Mustard Sauce 1
childs Coca Cola 1 Caesar salad w/ grilled
chicken
39
Going Back for Seconds Binary Model
• Initial conclusions
• Higher caloric intake will only cause him to gain
about 3 pounds over the month.
• Increased fat intake cant really say for sure
• Menu is more realistic not only is Spurlock able
to eat typical McDonalds fare, but he also
eats from the breakfast menu (which was actually
an implicit requirement in the original
experiment).

40
• Our next goal is to incorporate Spurlocks super
sizing condition into our model. We can do this
using Monte Carlo simulation.

41
• During Spurlocks original experiment, he was
asked to super size his meal a total of nine
times.

42
• During Spurlocks original experiment, he was
asked to super size his meal a total of nine
times.
• We can use this figure in our simulation to
determine best- and worst-case scenarios.

43
• Our simulation yields that Spurlock will super
size a minimum of zero times, an average of nine
times (as expected), and a maximum of 25 times
during the month.

44
• If Spurlock is asked to super size zero times, we
will not see a change in the results from our
binary model.

45
• If Spurlock is asked to super size nine times,
his total weight gain for the month is 4.4 pounds.

46
• If Spurlock is asked to super size twenty-five
times, his total weight gain for the month is 7
pounds.

47
48
Conclusions
• The basic integer programming model with which we
initially began is easy to implement and adapt.
• However, the bizarre combination of foods that
Spurlock would have to eat with this model was
highly unrealistic.
• Thus, the basic model, as it stands, is
inadequate for this type of situation.

49
Conclusions
• The binary model is also easy to implement and
• The binary constraint provided more variety in
Spurlocks menu, thus proving to be more like his
original experiment.
• The higher caloric intake did not drastically
affect Spurlocks weight gain, although the high
fat intake is a bit troubling.

50
Conclusions
• The super size model, even under the worst-case
scenario, yielded a menu that would cause
moderate weight gain for Spurlock.
• Despite our promising results, there are still
ways to improve upon our model.
• Can you think of what you might do differently?

51
Questions?