# Linear System Flyer

## Purpose

In this flyer I will be analysing the cost of a Samsung galaxy S5 with a cell plan in 2 different companies. The intention of this experiment is essentially based off of curiosity, but also has a basis of knowledge from the comparison in the 2 costs. What I've done is chosen a plan from each company with the same features and then compared it. They have different fixed and variable values, but both the plans contain the same features. It is necessary for the 2 phone plans to contain the same features so that the comparison made is fair. Other things I've done that lead the comparison to be fair is by choosing the same phone from the both the companies, picking the companies and rates all from the same city, and by choosing the appropriate companies itself. When I say choosing the appropriate companies itself I mean I chose the companies in such a way that it would be fair: Fido and Koodo are both companies that have been in the cell phone plan industry for the identical amount of years, therefore they have an equal amount of experience time. Also, both the companies are at the same economic condition with a similar amount of revenue and profit.

Here are the links for the 2 companies’ cell phone plan options:

Fido:

http://www.fido.ca/web/Fido.portal?_nfpb=true&_pageLabel=MonthlyPlans&getAvailablePlans=true

Koodo:

https://shop.koodomobile.com/plans/plans/index.html#wrapper

## Comparing Fido's and Koodo's Plan

Fido's:

The plan is the one that has 750 megabytes of data.

Fixed Cost: \$300 (the cost of the S5 on a 2 year contract like Fido's)

Variable Cost: Phone plan rate: \$49 (cost per month)

Slope: 49m

y-intercept: 300

Let C be the total cost for the plan

Let M be the amount of months the plan is used

C=\$49m+\$300

C-\$49m-\$300=0

X-Intercept (the m-intercept)

In the x-intercept, the y coordinate will be zero, or in this case the C coordinate will be zero:

0-49m-300=0

-49m=300

m=300/-49

m=-6.12

m=-6 3/25

Therefore the x/m-intercept is -6 3/25

Koodo's:

The plan is the one that has 750 megabytes of data.

Fixed Cost: \$275 (the original cost is 575, but it was reduced to 275 for a 2 year contract, the other plan for Koodo is also a 2 year plan)

Variable Cost: Phone Plan rate: \$50 (cost per month)

Slope: 50m

y-intercept: 275

Let C be the total cost for the plan

Let M be the amount of months the plan is used

C=\$50m+\$275

C-\$50m-\$275

X-Intercept (the m-intercept)

In the x-intercept, the y coordinate will be zero, or in this case the C coordinate will be zero:

0-50m-275=0

-50m=275

m=275/-50

m=-5.5

m=-5 1/2

Therefore the x/m-intercept is -5 1/2

## Organising the Plans in Tables:

Fido's:

C=\$49m+\$300

From this table chart, we know that the relationship of the numbers are linear; the total plan cost is going up by \$49 per person. From the table of values we also know that the relationship is partial because even without any months having passed by, the cost is \$300 (which is the cost of the phone).

Koodo's:

C=\$50m+\$275

From this table chart, we know that the relationship of the numbers are linear; the total plan cost is going up by \$50 per person. From the table of values we also know that the relationship is partial because even without any months having passed by, the cost is \$275 (which is the cost of the phone).

## The Point of Intersection:

In a Graph Form:
From using the graphing method, we know the point of intersection is (25,1525).

## The Point of Intersection:

Solving the equation through the means of substitution:

Koodo’s (1):

The equation for Koodos plan is:

C=\$50m+\$275

Fido’s (2):

The equation of Fido’s plan is:

C=\$49m+300

Let us substitute the value of m from equation 1 to equation 2 so that we can find the value of the the c coordinate in the point of intersection:

50m+275=49m+300

50m-49m=300-275

m=25

Now that we know the value of m in the point of intersection, we can find the value of c by substituting the value of m we just found into the 2 equations:

Koodo’s (1):

C=\$50m+\$275

C=50(25)+275

C=1250+275

C=\$1525

Fido’s (2):

C=\$49m+300

C=49(25)+300

C=1225+300

C=\$1525

Since the 2 answers of both the linear equations match out, we know that the c coordinate in the point of intersection is 1525.

Now that we know the c and m coordinates in the point of intersection, we know that at point (25,1525), the 2 cell phone plans will have the same total cost.

## The importance of the Point of Intersection:

The point of intersection or POI for short; allows one to closely observe and analyse so that they can make statements about their data. One statement from the POI we found between Koodo and Fido (25,1525), is that at these coordinates, the total cost of the 2 phone plans will be the same. Another statement we can make from the POI is that for any c coordinate higher than the POI, Fido's plan with the phone will be cheaper, but for any c coordinate lower than the POI, Koodo's plan with the phone will be cheaper (I can determine this from the visual aid we achieved by creating the graph).

## Conclusion:

In conclusion, we know that after 25 months, Koodo's and Fido's plan will have the same cost which is \$1525. Any amount of months higher than 25, Fido's plan will be cheaper, but any amount of months lower than 25 months, Koodo's plan will be cheaper. Therefore if you are a person that is usually into their phone plans longer than 2 years, Fido is your optimal choice between the 2. But, if you're a person that isn't on their plan for a long period of time, then Koodo is your optimal choice in this phone plan.

In the end, this investigation has taught me a lot about closely analyzing opportunities and tasks in life, to find the most optimal choice for me.