24/2018 Cousin Phil: Linear Models for Financial Analysis Cousin Phil: Linear Mo

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24/2018 Cousin Phil: Linear Models for Financial Analysis Cousin Phil: Linear Models for Financial Analysis How does someone like Bill Gates becomes so wealthy? We all know that poor sales mean financial rnuin, while stratospheric sales can create similarly spectacular profits. In this activity, you will create a quantitative model illustrating this, and use it to analyze and forecast An employer pays $3,000 per month for rent office space, and pays a total of 12 employees (including yoursel) $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 S18 (gross) per unit of work by an employee. A. Find your monthly salary S(x) as a function of x, the number of units of work you complete that month. B. If all of your co-workers produce/sell (on average) x units per month, find the monthly profit P(x) of your C. Suppose you complete 200 units per month. Find your monthly paycheck. D. Suppose all of your co-workers (on average) also complete 200 units per month. Find your boss Phil E Suppose you complete 300 units per month. Find your monthly paycheck. And also, supposing all of your F. How bad a month (how few a number of units of work completed) does it have to be for your employer to G. Due to the his revenues from the units of work you completed (service calls, sales, computer programs employer Phil Bates as a function of x. Bates' profits per month. co-workers (on average) also complete 300 units per month, find Phil Bates' profits on such months. make the same monthly salary you do? 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 (gros) for Phil Bates. 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? What if you produce/sell x-200 or 300 as in the carlier scenarios? allrond and heartily encouraged May not be used for anty other purpose withost w

Explanation / Answer

A ANS)

Assuming $1000 is paid to all 12 employees together because if $1000 is paid to each employess the company expenses would be more than its income and as a result firm would run into losses.

S(x) = Fixed salary + Variable salary

= $ 1,000 + $10(x)

were x = number of units of work completed for a month by you

B ANS)

No. of employees = 12 Rent = $3,000

$18 per employee per unit

Monthly Profit of Phil Bates as a function of x is given by

P (x) = Gross profit - expenses (i.e rent and salary of 12 employees)

= $ 18 *12(x) - $3,000-$(1000*12+10(x) )

were x is number of units of work produced by 12 employees together (i.e including yourself)

C ANS )

Monthly Paycheck

S(x) = Fixed salary + Variable salary

= $ 1,000+ $10(x)

were x = number of units of work completed for a month that is 200 units

S(x) = $1,000+ $10(200)

= $ 1,000 + $2000

= $ 3,000

D ANS)

No. of employees = 12 Rent = $3,000

P (x) = Gross profit - expenses (i.e salary and rent)

= $ 18*12(x) - $3,000- $( 1000*12+10(x) )

were x = 200 units (i.e including yourself)

P (x) = $18*12(200)-$3,000 -$ ( 1000*12+10(200) )

=$ 43,200 - $3,000-$ 14000

= $ 26,200

There Profits per month= $ 26,200

E ANS)

Your Monthly Paycheck

= $ 1,000 + $10(x)

were x=300 units

= $ 1,000 + $10(300)

=$ 4,000

Profit of Phil gates

= $ 18*12 (x) - $3,000- $( 1000*12+10(x) )

were x = 300 units (i.e including yourself)

= $ 18*12 (300) - $3,000- $( 1000*12+10(300) )

= $64,800-$3000-$15,000

= $ 46,800

F ANS)

Your monthly salary same as your employee is given as

$ 1,000 + $10(x) = = $ 18 *12(x) - $3,000-$(1000*12+10(x)

x = 81.63 units (approx)

So 82 units of work completed approximately makes your salary same as your boss.

G ANS)

2*[$ 1,000 + $10(x)] = [$ 18 *12(x) - $3,000-$(1000*12+10(x) ) ]

$2000+10x = [ 216x-3000-12000]

$1,000 = 206x-3000-12000

x= 91.39 or 91 units

10 TIMES MONTHLY WAGE

10*[$ 1,000 + $10(x)] = [$ 18 *12(x) - $3,000-$(1000*12+10(x) ) ]

10,000 +100x = 216x -3000-12000-10x

x = 235.85 or 236 units approximately

Hope this was helpful :)

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