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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
employee asked
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
employee asked
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
    items on McDonalds menu).

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
    this menu!

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
    realistic menu as well as add some variety to
    Spurlocks menu.

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
  • Spurlocks new menu

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
oatmeal raisin cookie 1 Bacon Ranch salad 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
Ready, Set, SUPER SIZE!
  • Our next goal is to incorporate Spurlocks super
    sizing condition into our model. We can do this
    using Monte Carlo simulation.

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

42
Ready, Set, SUPER SIZE!
  • 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
Ready, Set, SUPER SIZE!
  • 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
Ready, Set, SUPER SIZE!
  • If Spurlock is asked to super size zero times, we
    will not see a change in the results from our
    binary model.

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

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

47
Ready, Set, SUPER SIZE!
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
    adapt.
  • 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?
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