Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
430
© 2014 Pacific Crest
Scenario:
When planning to travel from NY to Miami you have the option to fly over the
range of a week. How much will it cost?
Step
Watch it Work!
1.
What is likely to change? The airline, number of connecting flights, and departure date can all
vary.
2.
How much will they
change?
The flight date ranges over the week. There are six major airlines.
The number of layovers is less than three.
3.
Test the inputs one at a
time
Using a trip-planning website we determine the possible range of
costs due to
1. Changing the airline
2. Changing the date
3. Changing the number of stops
4.
What effects do the
changes have?
Five of the six airlines are similar in price while the last is more
expensive. The dates closer to the weekend are more expensive
than during the week. Decreasing the number of stops increases
the cost.
5.
Which input has the most
impact?
The greatest difference in cost results when we first avoid the
expensive airline, then travel during the weekdays, then allow two
stops.
6.
Analyze the results
The prices range from $124 to $315
7.
Interpret your findings
The what-if modeling suggests that we choose to leave whenever
the total cost is minimized, provided we don’t mind the layover.
YOUR
TURN!
Scenario:
How long would it take you to drive across the U.S.? Start at New York and
end at Los Angeles. Consider variations in the route, speed, and time spent
refueling, eating, and resting.
O
ops
! A
voiding
C
ommon
E
rrors
●
Assuming the input with the largest range of possibilities will cause the greatest change in the
results
Example
: A student incorrectly assumes that the greatest increase in a population model will be
found by increasing the initial population.
Why?
Though the increase in initial population is greater than any realistic variation in the
growth rate constant, the small changes in the growth rate constant lead to much
larger populations at a later time.
●
Assuming the extreme values of an output occur when the inputs take on extreme values
Example
: To optimize horizontal distance, the angle of release for a projectile should be 45°
Why?
The angle between the direction you throw an object and the horizon can range
between 0° and 90°, but these extreme values result in sub-par horizontal distances