# Piecewise Function Word Problem

#### mwass

##### New member
I really dislike word problems because I can't seem to get the information in the right order. I'm wondering if anyone can help me out.

Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 7 pounds, they charge $1.25 per pound. For packages weighing between 7 and 13 pounds, they charge$ 2.25 per pound. If packages weigh 13 pounds or more, they charge $3.5 per pound. IPS refuses to ship any parcel weighing more than 98 pounds. There is also a flat fee of$ 1 for all deliveries and an additional fee of $3 for all deliveries weighing 13 pounds or more. Complete the following description of a piecewise function so that is describes the shipping costs [FONT=MathJax_Math-italic]C[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][/FONT] in dollars as a function of the weight xin pounds. So far I have: (1.25 + 1) if x is in the interval (-inf,7] (2.25 +1) if x is in the interval (7,13) (3.50+1+3) if x is in the interval [13,inf) Apparently everywhere is wrong. So I could use some help figuring out why. It would be very much appreciated. #### stapel ##### Super Moderator Staff member Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 7 pounds, they charge$ 1.25 per pound. For packages weighing between 7 and 13 pounds, they charge $2.25 per pound. If packages weigh 13 pounds or more, they charge$ 3.5 per pound. IPS refuses to ship any parcel weighing more than 98 pounds. There is also a flat fee of $1 for all deliveries and an additional fee of$ 3 for all deliveries weighing 13 pounds or more.

Complete the following description of a piecewise function so that is describes the shipping costs [FONT=MathJax_Math-italic]C[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][/FONT] in dollars as a function of the weight xin pounds.

So far I have:

(1.25 + 1)
if x is in the interval (-inf,7]
(2.25 +1)
if x is in the interval (7,13)
(3.50+1+3)
if x is in the interval [13,inf)

Apparently everywhere is wrong.
I'm sorry, but I don't understand what you mean by this last statement? Also, why are you allowing weights to be negative, and ignoring the maximum-weight restriction given in the exercise?

#### ksdhart

##### Full Member
I'm going to go out on a limb and say that the "everywhere is wrong" part means you either showed your answers to your instructor or inputted them into an online interface, and were told that the solutions you've given were incorrect. Now, aside from Stapel's questions about why you're allowing negative weights and weights more than the problem specifies... you have three solutions and they all have the same, very simple to correct, error. As written, you're saying the solutions are:

For packages less than 7 pounds, the cost to ship the package is (1.25 + 1). In other words, for a package weighing up to 7 pounds, the person will pay exactly $2.25. For packages between 7 and 13 pounds, the cost to ship the package is (2.25 + 1) or exactly$3.25.
For packages more than 13 pounds, the cost is (3.5 + 1 + 3) or exactly $7.50 Can you see now why your answers are wrong? If you wanted to make a cost function where the person pays$1.25 per pound, plus the 1 dollar flat fee, what would you do? Apply similar logic to the other two parts and you're good.

#### mwass

##### New member
English is not my first language so it slipped with wrong word.

Would it be more like this:

(1.25 + 1) if x is in the interval (0,7]
(2.25 +1)
if x is in the interval (7,13)
(3.50+1+3)
if x is in the interval [13,98] Anything past 98 pounds is excluded

#### stapel

##### Super Moderator
Staff member
English is not my first language so it slipped with wrong word.

Would it be more like this:

(1.25 + 1) if x is in the interval (0,7]
(2.25 +1)
if x is in the interval (7,13)
(3.50+1+3)
if x is in the interval [13,98] Anything past 98 pounds is excluded
How does the value of x affect your values? (Hint: Since "x" is not currently included in any of your "value" expressions, it cannot have any effect. This omission should perhaps be corrected.)