Piecewise functions (I need help ASAP!)

[megadeth95]

Hello, I need help with this problem, I don't know what to do.


1. Write a piecewise-defined function representing the cost of shipping x pounds with Packages Inc.

Package Inc.

up to 10lb -----> $ 2.00 per pound
10-25 ----------> an additional $ 1.50 for each pound over 10 pounds.
over 25lb ------> an additional $ 1.10 for each pound over 25 pounds.


2. When is Packages Inc. the cheapest?

This is what I did so far:

y=2x if 0<x<10

I don't know what to do for the other two.

Thanks in advance

 

[megadeth95]

Your teacher didn't explain?
Go learn:
http://www.google.ca/#hl=en&cp=0&gs....,cf.osb&fp=7df80a66766b08bf&biw=1009&bih=563

Actually, my teacher DID explain this and I know piecewise functions. The only problem that I have is that I don't know how to write the piecewise function for these:

Pounds

10-25 ------------------------> an additional $ 1.50 for each pound over 10 pounds.

over 25lb -------------------> an additional $ 1.10 for each pound over 25 pounds.


I did this so far:

y=x-8.5 if 10 < x ≤ 25

y=x-23.9 if x>25

Is this right??

thank you

 

[wjm11]

up to 10lb -----> $ 2.00 per pound
10-25 ----------> an additional $ 1.50 for each pound over 10 pounds.
over 25lb ------> an additional $ 1.10 for each pound over 25 pounds.


2. When is Packages Inc. the cheapest?

This is what I did so far:

y=2x if 0<x<10

You got off to a good start. You correctly used the "$2.00 per pound" as the slope: y = 2x.

 

[megadeth95]

You got off to a good start. You correctly used the "$2.00 per pound" as the slope: y = 2x. But now the price is going up for a heavier package; if it is "an additional $1.50", that just means you add 1.50 to the initial amount (2.00), for a total of $3.50 per pound. Now the slope is 3.5 . Make sense?

ohhhhhh I get it now! , so it has to be:

y=3.5x if 10 < x ≤ 25

y=3.1x if x>25

Thank you so much for your help!

One last question, it says "up to 10lb"

does it have to be like this o<x<10
or
like this: 0<x≤10

that's all, thx in advance!

 

[wjm11]

ohhhhhh I get it now! :grin:, so it has to be:

y=3.5x if 10 < x ≤ 25

y=3.1x if x>25

Thank you so much for your help!

One last question, it says "up to 10lb"

does it have to be like this o<x<10
or
like this: 0<x≤10

Good thinking about your constraints. I would interpret "up to 10lb" as 0 ≤ x ≤ 10 because of what is said in the second statement.

The second statement "10-25 ----------> an additional $ 1.50 for each pound over 10 pounds" clearly says this applies only "over" 10 pounds, so this means 10 < x ≤ 25.

 

[megadeth95]

Thanks for your help!!

 

[soroban]

Hello, megadeth95!

1. Write a piecewise-defined function representing the cost of shipping \(\displaystyle x\) pounds with Packages Inc.

up to 10 lbs.. . . $2.00 per pound
10 to 25 lbs.. . . an additional $ 1.50 for each pound over 10 pounds.
.over 25 lbs. . . .an additional $1.10 for each pound over 25 pounds.

For the first 10 pounds, the cost for \(\displaystyle x\) pounds is: \(\displaystyle 2x\) dollars.

For 10 pounds, the cost is $20.
For each addition pound, it costs $1.50 per pound.
For the interval \(\displaystyle (10,25]\), the cost is:
. . \(\displaystyle C(x) \:=\:20 + 1.5(x-10) \:=\:1.5x + 5\) dollars.

For 25 pounds, the cost is $42.50.
. . $20 for the first 10 lbs,
. . then \(\displaystyle \$1.50 \times 15 \,=\,\$22.50\) for the next 15 pounds.
For each addition pound it costs $1.10 per pound.
For the interval \(\displaystyle (25,\infty)\),
. . the cost is: .\(\displaystyle C(x) \:=\:42.50 + 1.10(x-25) \:=\:1.10x + 15 \) dollars.

Therefore: .\(\displaystyle C(x) \;=\;\begin{Bmatrix}2x && 0 < x \le 10 \\ 1.5x + 5 && 10 < x \le 25 \\ 1.10x + 15 && x > 25 \end{array}\)

2. When is Packages Inc. the cheapest?

I'll let you work it out . . .

 

[wjm11]

Megadeath,

Soroban has given you a correct analysis. I misinterpreted part of the problem, and my comments regarding slope were incorrect. (Thanks, Soroban!)

 

[megadeth95]

Hello, megadeth95!


For the first 10 pounds, the cost for \(\displaystyle x\) pounds is: \(\displaystyle 2x\) dollars.

For 10 pounds, the cost is $20.
For each addition pound, it costs $1.50 per pound.
For the interval \(\displaystyle (10,25]\), the cost is:
. . \(\displaystyle C(x) \:=\:20 + 1.5(x-10) \:=\:1.5x + 5\) dollars.

For 25 pounds, the cost is $42.50.
. . $20 for the first 10 lbs,
. . then \(\displaystyle \$1.50 \times 15 \,=\,\$22.50\) for the next 15 pounds.
For each addition pound it costs $1.10 per pound.
For the interval \(\displaystyle (25,\infty)\),
. . the cost is: .\(\displaystyle C(x) \:=\:42.50 + 1.10(x-25) \:=\:1.10x + 15 \) dollars.

Therefore: .\(\displaystyle C(x) \;=\;\begin{Bmatrix}2x && 0 < x \le 10 \\ 1.5x + 5 && 10 < x \le 25 \\ 1.10x + 15 && x > 25 \end{array}\)




I'll let you work it out . . .

Thank you sooooo much!!!!you saved my day!
I knew that something was not right. This problem was quite hard for me!

Once again, thank you for helping me guys, I really appreaciate it!!

Best Regards

megadeth95