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© 2014 Pacific Crest
175
Assumptions:
●
Every square foot of space has the same value.
●
Students have an equal share and financial
responsibility for the common area.
●
A private room is worth $50 more per month.
●
Only two rooms can be used as bedrooms.
●
Two students will share the larger bedroom.
●
Room assignments will be made first by
choice, then by a random drawing.
●
Any two students could share a room.
Sub-problems
:
The following sub-problems were identified:
1. What is the cost of each room per month? 2. How should rooms be chosen?
Model for cost of each room
:
Here is the model developed using the stated information and assumptions:
The one student with a private room will pay $50/month premium for that room. This leaves $650
per month in rent to be paid for the remaining area of the house by all three students.
Since every one of the 1,720 square feet of the house has equal value, the cost per square foot will be
$650 divided by 1,720 square feet = $0.3779 per square foot (this figure can be used to calculate the
financial worth of the square footage of each bedroom as well as the common area).
Each person will be responsible for one third of the cost of the common area. The two people who
share the larger bedroom will each be responsible for half of the cost of this bedroom. The person
who has the private room will be responsible for the value of the entire bedroom and pay a $50
premium for the privacy.
Model for choosing
:
Students choose the room they want in writing. A person who chooses a room that is not chosen by the
other students gets that room. When there is competition for the same room, a random drawing selects
the student who will get the room. Those students not assigned will choose again and go through the
steps until all the room positions are assigned.
Integration
:
Calculate the cost of each bedroom plus the common area.
Small bedroom with an area of 270 ft
2
cost/month = 270 ft
2
× 0.3779 dollars per ft
2
=
$102.03
Large bedroom with an area of 360 ft
2
cost/month = 360 ft
2
× 0.3779 dollars per ft
2
=
$136.04
cost/month per student for the large bedroom = $136.04 divided by 2 =
$68.02
Common area = total house area minus total bedroom area
common area = 1,720 ft
2
– 270 ft
2
– 360 ft
2
=
1090 ft2
4.2 Applying the Problem Solving Methodology