Question

"The start up cost of a company is 150,000$. It costs $.17 to manufacture each headset/ graph the function that represents the average cost of a headset. how many must be manufactured to result in a cost less then 5$ per headset."

If someone could please help, that'd be great. I don't need helping graphing, but if you could show me how to set up the equation, I'd love it! Thanks. :)

Answer 1

@phi, can you please help?

Answer 2

one way to think about it:

i f you made one headset, it would cost 150,000 (the start-up cost) and then another 0.17 to make the headset.

if you made 2 headsets, it still costs 150,000 for start-up, and 2*0.17 to make the two.
the total cost to make the 2 headsets is T= 150,000 + 2*0.71
the average cost (or cost per headset) is T/2

can you use these ideas to figure out the average cost for N headsets ?

Answer 3

you want to find an equation to answer
how many must be manufactured to result in a cost less then 5$ per headset."

it would look something like
T/N < 5

where T is the total cost to make N headsets, and N is the number of headsets.

Answer 4

The cost is to start with (as you have spent 150,000 that will give you a minus sign)
\[m=-150,000\]
Production cost p:
\[p=-0.17x\]
And the cost to consumer is:
\[h=5x\]
where x is number of units.

The linear function for this companys economy would then be something like...
y= PROFIT-COST

Did it help? :)

Answer 5

@phi, where did you get 2 in the average cost? = T/2??

Answer 6

that was an example for just 2 headsets

you have to extend the idea to N head sets

Answer 7

Also, @kalph , you said y=p-c but which cost specifically is being subtracted? You mentioned 3...

Answer 8

Okay, so then my equation should look like:

5=150,000 +1.7x and we solve for x. Does that look right @Phi?

Answer 9

no. what are the chances 5 = 150,000 + more stuff ?

The idea is write down how much it costs to make N headsets. The way to figure that out is write down how much it costs to make 1 headset, or 2 or 3... and llook for the pattern.

that is the first step.

Answer 10

okay, so T/n<5
t/1<5, n =1; t=5
t/2<5, n=2; t=10
t/3 <5, n=3; t=15

So we can conclude that it varies directly, right? and that's a step in the right direction?

Answer 11

the cost is the startup cost plus the manufacturing cost.

the cost to build 1 headset is a lot: 150,000.17

Answer 12

So we know the equation is y=kx or y/x=k
y=t=150,000 (total cost available?)
x=n.17=Cost per set being manufactured.
This fraction when simplified should equal 5, right?
150,000/n.17 =5

Answer 13

why is the cost to build a headset 150,000.17?? That exceeds the budget- or am I misunderstanding something?

Answer 14

"The start up cost of a company is 150,000$. It costs $.17 to manufacture each headset/ graph the function that represents the average cost of a headset.

You include the cost to start-up.

Answer 15

okay. Thanks.

Answer 16

Nothing i'm setting up is working out. Can you please give me the equation and what each variable is so I can solve? I'd really appreciate it. :)

Answer 17

@phi?? Hello??

Answer 18

what is the cost if you made *only* 3 headsets, including start up costs?

Answer 19

150,000.51

Answer 20

now if it were N headsets, what would you write down ?

Answer 21

150,000 + n(.17) right? @phi
But what does it equal?? Like you said, it can't equal 5.

Answer 22

that is the cost to make n headsets

how many must be manufactured to result in a cost less then 5$ per headset. ?

what is the total cost of n headsets if each cost $5 ? answer: 5n

you want the total cost to be less than 5n

Answer 23

150,000 + n(.17) < 5n


that is now quite the function they are asking for.
graph the function that represents the average cost of a headset

if the total cost is 150,000 + n(.17) what is the average cost? the average is the total divided by n

so they want you to graph
y= (150,000 + x(.17) )/x= 150,000/x + 0.17
(I changed n to x, so you can plot it on an x-y graph)

Answer 24

wolfram can do it
http://www.wolframalpha.com/input/?i=plot++y%3D%28150%2C000+%2B+x%28.17%29+%29%2Fx+where+1%3C+x+%3C+40%2C000

Answer 25

It should be obvious that it will take a lot of headsets to get the average cost down to $5.00

Answer 26

if they cost nothing to make (meaning ignore the 0.17)
then we could divide $5 into 150,000 to get 30,000 headsets
It will take a bit more than that because they do cost a little bit to make each one.

but you can solve
150,000 + n(.17) < 5n
add -0.17n to both sides
150,000 < 5n - 0.17n
150,000 < (5-0.17) n (factor out the n
150,000 < 4.83 n (simplify 5-0.17)
divide both sides by 4.83
150,000/4.83 < n
31055.9006 < n

that means
n> 31056

Answer 27

While you were typing that out, I was solving and got the same thing. I know this was hard cause I wasn't exactly getting it, but I do now!! Thank You SO much!! :D

Answer 28

Can you just read through a word problem for me and tell me if it's a trick question?? I already have the answer, but I'd love if you'd just check my work. :) @phi

Answer 29

did you post it?