Cousin Phil: Linear Models for Financial Analysis
How does someone like Bill Gates becomes so wealthy? We all know that poor sales mean financial
ruin, while substantial sales can create similarly spectacular profits. In this activity, you will create a
quantitative model illustrating this, and use it to analyze and forecast earnings for a company.
An employer pays $3,000 per month to rent office space, and pays a total of 12
employees (including yourself) $1,000 per month plus a bonus of $10 for each unit of
work completed by the worker that month. Suppose also that your employer makes $18
per total units of work by all employees.
Just the Facts:
Cost to rent out office space per month:
Total # of employees:
A. Find your monthly salary S(x) as a function of x, the number of units of work you complete that
month.
S(x) =
where x = units of work
Graph this line. Identify the slope, x-intercept, and y-intercept.
B. If all of your co-workers produce/sell (on average) x units per month, find the monthly profit P(x) of
your employer Phil Bates as a function of x.
Amount paid out to workers each month:
Amount paid for rent each month:
Amount earned each month:
P(x) =
Graph this line. Identify the slope, x-intercept, and y-intercept.
C. Suppose you complete 200 units per month. Find your monthly paycheck.
S(x) = S(200) =
D. Suppose all of your co-workers (on average) also complete 200 units per month. Find your boss Phil
Bates' profits per month.
P(x) = P(200) =
E. Suppose you complete 300 units per month. Find your monthly paycheck. And also, supposing all of
your co-workers (on average) also complete 300 units per month, find Phil Bates' profits on such
months.
Your monthly paycheck: S(300) =
Phil Bates’ monthly profits: P(300) =
F. How bad a month (how few a number of units of work completed) does it have to be for your
employer to make the same monthly salary you do?
G. Due to the his revenues from the units of work you completed (service calls, sales, computer
programs written, etc), your employer Phil Bates (following his wealthier cousin Bill) is able to now
rent a bigger office ($10,000 per month), and employ 50 employees, each one still getting $1,000 per
month plus $10 per unit of work completed, and again each unit of work completed makes $18 for
Phil Bates.
Just the Facts:
Cost to rent out office space per month:
Total # of employees:
New Equations
S(x) =
where x = units of work
P(x) =
H. How many units (x) would you and your co-workers have to complete each month before Phil's
(monthly) profits are double your monthly wage? Ten times your monthly wage?
Double your monthly wage: P(x) = 2S(x)
Ten times your monthly wage:
I. What if you produce/sell x=200 or 300 as in the earlier scenarios?
S(200) =
S(300) =
Computer Application
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Go to www.shodor.org/interactivate/activities/slopeslider. The current equation is y = (0)x + 0.
Move the blue, purple, and green slider bars around a little bit.
Record your current equation. This is your starting equation.
Starting Equation: _____________________
Y-Intercept: ______________
X-Intercept: ______________
Slope: ___________________ * You can use the blue slider bar to get two points on
A: _________ B: _________
your line to help you find the slope. *
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Move the purple slider bar. Record your current equation.
Starting Equation: _____________________
Y-Intercept: ______________
X-Intercept: ______________
Slope: ___________________
A: _________ B: _________
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Move the purple slider bar again. Record your current equation.
Starting Equation: _____________________
Y-Intercept: ______________
X-Intercept: ______________
Slope: ___________________
A: _________ B: _________
Did you notice anything? What?
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Move the green slider bar. Record your current equation.
Starting Equation: _____________________
Y-Intercept: ______________
X-Intercept: ______________
Slope: ___________________
A: _________ B: _________

Move the green slider bar again. Record your current equation.
Starting Equation: _____________________
Y-Intercept: ______________
X-Intercept: ______________
Slope: ___________________
A: _________ B: _________
Did you notice anything? What?
Homework – Write a paragraph explaining your understanding of the relationship between the graph
and the slope-intercept form of an equation. At least five thoughtful sentences. Why is the slopeintercept form of an equation so helpful? Why would this form of an equation be preferred over other
forms?