Math Is Fun Forum

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,214

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

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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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,214

Re: First-class Mail

Yes, that's right.

Bob

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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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

Re: First-class Mail

Yes, that's right.

Bob

It took me an hour to figure it out.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah