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© 2014 Pacific Crest
163
Step
Watch it Work!
7.
Integrate
solutions
Given the models, it looks like one large pizza is the best deal. But let’s look at
some other options.
If Chuck buys two small pizzas at $10, they only get 32
π
of pizza, vs. 64
π
for
$1 more. Not a good deal.
If he buys a small and a medium pizza at $13, they get (16 +36)
π
= 50
π
; less
than one large pizza and for more money.
It looks like buying a large pizza makes the most sense and Chuck has enough
money as well.
8.
Test & validate Is this convincing? It does appear that a large pizza is the way to go.
9.
Generalize the
solution
The method of finding a common comparison, in this case units of pizza (via
area) per dollar, can be generalized. Often, when buying items, one needs to
make this kind of comparison. Sometimes, you may be surprised. Is 5 cans for
a $1 better than 19¢ per can? Is an all-day ticket at an amusement park for $40
better than $2 per ride?
10. Communicate
the solution
Chuck and Elissa should order a large pizza for $11, and Chuck will have the
leftovers for a tasty breakfast.
O
ops
! A
voiding
C
ommon
E
rrors
●
Not defining the problem clearly or precisely enough
Example
: Do I have enough money to go out tonight?
Why?
What does “going out” mean? Tacos at a local drive-thru or is tonight the prom?
And if it
is
prom night, might you not need to define things even more? What about
flowers? Transportation? Am I responsible for dinner? Tickets? Do I need to buy new
clothes? It is not possible to solve a problem that is not defined.
●
Missing a significant issue that changes the nature of thinking about the problem
Example
: Preparing an Easter Dinner for three families in the neighborhood
Issues
1) Size of their families
2) Constraints to diet (allergies, etc.)?
3) Budget limits
4) Time of day
5) Is there a good location for either a sit down meal or buffet?
And those are important issues. But one that was missed was the capacity for cooking
and baking. If the power of the circuit can only support the oven and two burners,
then preparing a large meal for many people could take much longer than usual (thus
possible affecting the time and location) and could easily affect the menu (which can
have everything to do with your budget).
Why?
There are often contextually buried issues that must be identified in order to solve the
problem that exists in that context.
4.1 The Problem Solving Methodology