Your task for this discussion is as follows:
- Research an advertised truck rental price plan that does not include unlimited miles and provide the details of the advertisement. (e.g., $50/day with 200 miles included and $0.10 per additional mile.)
- Create your own similar truck rental price plan with different values. Be sure to not use the exact same values used in a previous post.
- Based on your plan, write an equation that can be used to determine the daily cost, D(t) of the rental when t miles are needed, and use that equation to calculate the total cost when 300, 1,000, and 2,000 miles are used.
- In your responses to peers, compare the total costs you calculated in Part 3 with those of at least two peers. Discuss the differences you notice and how they could have been foreseen by just comparing the formulas.
From my investigation, I found that the daily rate for a rental truck goes for $19.95 with 50 miles included
and a charge of $1.29 per mile. With these numbers I have formed my rates to be set at a daily rate for $18
with 60 miles included and a charge of $1.50 per mile. Going with function notation, we will say
D(t) = m (t – 60) + b will be our formula to figure out our overall daily cost. The constant b will
represent the daily flat-rate. The variable t will represent the amount of miles driven. Finally our slope m
will represent the sur-charge of each additional mile driven.
300 Mile Daily Cost
D(t) = m(t – 60 + b
D (300) = 1.5 (300 – 60) + 18
D (300) = 1.5 (240) + 18
D (300) = 360 + 18
D (300) = 378
=
$378 is the cost for a one day rental that has been driven for 300 miles.
1,000 Mile Daily Cost
D(t) = m (t – 60) + b
D (1000) = 1.5 (1000 – 60) + 18
D (1000) = 1.5 (940) + 18
D (1000) = 1410 + 18
D (1000) = 1428
$1,428 is the cost for a one day rental that has been driven for 1,000 miles.
2,000 Mile Daily Cost
D(t) = m(t – 60) + b
D (2000) = 1.5 (2000 – 60) + 18
D (2000) = 1.5 (1940) + 18
D (2000) = 2910 + 18
D (300) = 2928
$2,928 is the cost for a one day rental that has been driven for 2,000 miles.
At U-Haul, the cost of renting a 10′ Truck for 2 days between Federal Co, and Raton, NM is $271 with
258miles included. $0.43/mile for extra mileage.
My own: $250 with 300 miles included, and $0.35 for extra mileage.
These are the rates:
Where D(t) is the daily cost and t is the total miles covered
D(t)=250+0.35(t-250)
1. When 300 miles are used, the daily cost D(t) is:
D(300)=250+0.35(300-300)
D(300)=250
2. When 1000 miles are used, the daily cost D(t) is:
D(1000)=250+0.35(1000-300)
D(1000)=495
3.When 2000 miles are used, the daily cost D(t) is:
D(2000)=250+0.35(2000-300)
1/2000=845