Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

First-class Mail

In 2009 the U.S. Postal Service charged $1.17 postage for first-class mail retail flats (such as an 8.5 by 11 envelope) weighing up to 1 ounce,plus $0.17 for each additional ounce up to 13 ounces. First-class rates do not apply to flats weighing more than 13 ounces. Develop a model that relates C, the first-class postage charged, for a flat weighing x ounces. Graph the function.

I need help setting up the correct function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: First-class Mail

Mathematically, this is similar to the truck charge question.  First summarise the info.

0 < weight ≤ 1              fixed charge of 1.17
1 < x ≤ 13                    0.17 per ounce

So between x=0 and 1 the graph will be a horizontal line as the charge is fixed and doesn't vary with x.

After that the additional cost starts to go up in a straight line with gradient 0.17 .

The graph stops when x=13

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: First-class Mail

Mathematically, this is similar to the truck charge question.  First summarise the info.

0 < weight ≤ 1              fixed charge of 1.17
1 < x ≤ 13                    0.17 per ounce

So between x=0 and 1 the graph will be a horizontal line as the charge is fixed and doesn't vary with x.

After that the additional cost starts to go up in a straight line with gradient 0.17 .

The graph stops when x=13

Bob

I don't understand your summary here.

You said:

0 < weight ≤ 1              fixed charge of 1.17
1 < x ≤ 13                    0.17 per ounce

Where did 0 and 1 come from?

Where did 1 and 13 come from?

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: First-class Mail

Mathematically, this is similar to the truck charge question.  First summarise the info.

0 < weight ≤ 1              fixed charge of 1.17
1 < x ≤ 13                    0.17 per ounce

So between x=0 and 1 the graph will be a horizontal line as the charge is fixed and doesn't vary with x.

After that the additional cost starts to go up in a straight line with gradient 0.17 .

The graph stops when x=13

Bob

Wait a minute.  I think I got it.
I got a piecewise function.

Let C(x) = piecewise function

C(x) = {1.17, if 0 < x ≤ 1...top portion of function.

C(x) = {1.17 + 0.17(x - 1), if 1 < x ≤ 13...bottom portion of function.

Does my model accurately captures the pricing structure for first-class mail retail flats as described in the problem statement?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: First-class Mail

Yes, that's right.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: First-class Mail

Yes, that's right.

Bob

It took me an hour to figure it out.