# MOVING COMPANIES

### Linear System Flyer Project

## By: Tina Tsan

## Company A

Company A charges customers an upfront cost of $40 to pay for the move, truck fees, labour cost, etc and $20 for every hour it takes to move.

Variable Cost [slope]: $20/hour

m= 20 (slope)

b= 40 (fixed cost)

therefore...

y=mx+b form: y=20x+40

ax+by=c form: 20x-y+40=0

## Company B

Company B charges an upfront cost of only $20 for the move, truck fees, labour costs, etc but $50 for every hour it takes to move.

Variable Cost [slope]: $50/hour

m= 50 (slope)

b= 20 (fixed cost)

therefore...

y=mx+b form: y=50x+20

ax+by=c form: 50x-y+20=0

## click below to see full graph

## INTERSECTION

20x-50x=20-40

-30x=-20

x=-20/-30

x=0.67

We can now substitute x=0.67 into either equation to find y.

y=20x+40

=20(0.67)+40

=13.4+40

=53.4

Therefore we can conclude that the coordinates of the intersection is (0.67,53.4) OR (64/100, 267/5).

[0.67 hours, $53.40]

## Significance

For example, in our case, if you look at the graph above, you can see Company B is cheaper than Company A. But after they intersect, Company A is cheaper than Company B. This means that Company B is cheaper and more ideal for moves that take less than 0.67 hours whereas Company A is more ideal for moves longer than 0.67 hours.

In conclusion, knowing the intersection helps customer determine the best deal for them depending on how long it takes for them to move. [How long it takes to move depends on how much stuff they have]