Question

Truck Alpha initially costs $413 more than Truck Beta, but it consumes 0.03 liter/km versus 0.06 liter/km for Beta. Both trucks last 9 years, and Beta's salvage value is $144 smaller than Alpha's. Fuel costs $1.71 per liter. Other things being equal, beyond how many kilometers of use per year does Alpha become preferable to Beta?

Answer 1

@DanJS

last problem

Answer 2

C(x)_alpha = 413 + 0.03X
C(x)_Beta = 269 + 0.06X

set equal we get 413 + 0.03X = 269 + 0.06X, X=1600liter/Km

1600liter/km*(1/1.71liter) = 935 km

Answer 3

@DanJS

Answer 4

@DanJS

Answer 5

the question asks when does the cost to operate both trucks have the same value in terms of kilometers, cost as a function of kilometers

Answer 6

C = cost
X = kilometer

C(X) = some function

Answer 7

Hold on should I first try to determine what the function is as far as what is x and what is y?

Answer 8

k so just have to keep track of these things they tell you , first A has $413 over B

A-- C(X) = 413
B-- C(X) =

Answer 9

okay

Answer 10

you want to have the cost in terms of kilometers, that is what they are asking for kilometer value

Answer 11

okay

Answer 12

sorry i am here...

the gas for each will cost
\[\frac{ X~km }{ 1 }*\frac{ 0.03~L }{ 1~km }*\frac{ $1.71 }{ 1~L}\]

Answer 13

No worries. Let me analyze this for a bit

Answer 14

change the 0.03 to 0.06 for B

Answer 15

cost function, each term should be in dollars, see that has dollars, given the number of km driven X

Answer 16

A-- C(X) = 413 + (1.71*0.03)*X

B-- C(X) = (1.71*0.06)*X

Answer 17

Okay i see where you are getting at

for a: 0.051x
for b: 0.1026x

X is in terms of dollars

Answer 18

no X as you defined is km, c(X) is cost in dollars dependent on km driven

Answer 19

Oh I thought the km would cancel but you are referring to x being km

so it would be 0.051km*X
and 0.1026km*X

Answer 20

B has a smaller sell back value at the end of the 9 years $144, so add that to B

A-- C(X) = 413 + (1.71*0.03)*X

B-- C(X) = (1.71*0.06)*X + 144

Answer 21

right X is km, notice the 3 terms and how X km cancels from that, leaving $

Answer 22

Yes it leaves dollars. That is why I was assuming the x represented dollars but it doesn't because this is a function of C dollars respect to X a distance

Answer 23

so they are 2 lines, B starts cheaper overall, but increases faster, and will overtake A at some point... (X, C(X))

Answer 24

we tack the 144 on B because it will sell for 144 at the end of it's life? Why wouldn't we take the initital cost and subtract it from the 144 instead to obtain 269 and tack that on instead?

Answer 25

B is $144 less than A value to sell back, B will get 144 less back than A, so add the 144 onto B, or Subtract 144 from A, either is good

Answer 26

okay okay I see so my thoughts were correct but you solved it differently. Okay thanks.

Answer 27

x = 5243.66 km

Answer 28

A-- C(X) = 413 + (1.71*0.03)*X
B-- C(X) = (1.71*0.06)*X + 144

i trust ya on that value.. ha

Answer 29

Okay thanks for your help. When are you normally on OS? I am not very active on here usually. I use the site mostly when I get stuck.

Answer 30

actually since it is cost functions, it would be better to put the 144 as -144 on A instead, since they getting money back
but since we comparing the relative cost of A and B, either way is fine

Answer 31

usually when i can, sometimes alot, sometimes not for weeks

Answer 32

Okay well I appreciate the explanation to solving the question. I will probably redo the problem on paper and re evaluate what we discussed more.

Answer 33

yeah , that is better than a discussion, i could post the whole solution as one response, but that wouldnt help

Answer 34

I disagree. The discussion helps me understand the problem more. Discussing how to set it up and what do analyze help me the most.

Answer 35

i mean, you writing it down is better, do that ..heh