Rational Function Help

alz921 · 2010-05-16 15:13:56

I have a type of problem that i need some major help on. I am not getting at all how to do this. the problem is....

It costs a company $30,000 to begin production of a good, plus $3 for every unit of the good produced. Let x be the number of units produced by the company.

a.) Find a formula for C(x), the total cost for the production of x units of the good.
b.) Find a formula for the company's average cost per unit, a(x).
c.) Graph y=a(x) for 0< x <(or equal to) 50,000, 0<(or equal to) y <(or equal to)10.
d.) Explain in economic terms why the graph of a has the long-run behavior that it does.
e.) Explain in economic terms why the graph of a has the vertical asymptote that it does.
f.) Find a formula for a^-1(y). give an economic interpretation of a^-1(y).
g.) The company makes a profit if the average cost of its good is less than $5 per unit. Find the minimum number of units the company can produce and make a profit.

Steps to find the answers will be greatly appreciated.

Thanks,
alz92

bobbym · 2010-05-16 15:29:24

Hi alz921;

It would help if you had shown what you have done so far. Let's work them together.

a) The cost function is C(x) = 30000 + 3x

What do you think about b)?

alz921 · 2010-05-16 15:38:11

well i havent done anything on it so far cause i didnt know where to start to be honest. i am not sure what a(x) means. can you explain to me what it means and ill try it out myself

bobbym · 2010-05-16 15:43:26

Hi;

The average cost is just this, supposing he makes 10 of these things. His average cost is (30000 + 30) / 10. Does that help you a little. Try your own and bring back your results to me.

alz921 · 2010-05-16 15:49:17

ok so would B. is 30000 + 3x/ x?

bobbym · 2010-05-16 15:52:29

Hi;

Yes, that is correct, with x the number made!

How about c)

alz921 · 2010-05-16 15:56:51

I graphed it....for d.) it has that long run behavior because in the numerator the leading term is 3x and the denominator is just x so the ratio is 3/1.

bobbym · 2010-05-16 16:05:16

Hi;

Whoa! That is not the numerator. The function is (30000 + 3x) / x , not 30000 + (3x) / x.

alz921 · 2010-05-16 16:06:32

yes i know im saying the leading term of the numerator is 3x correct so the ratio of the long-run behavior is 3/1

bobbym · 2010-05-16 16:08:54

Yes, you could say that. Later in asymptotic analysis you will see that the 3x drowns out the 30000. very good!

alz921 · 2010-05-16 16:10:31

alright good. can we move to part f.) cause this is where im the most confused. inverses are not my thing.

bobbym · 2010-05-16 16:15:21

Read this:

http://www.mathsisfun.com/sets/function-inverse.html

Then you will explain it to me.

alz921 · 2010-05-16 16:25:06

ok so i took a(x) and i went the opposite direction so i multiplied the x in the denominator to the left side then subtracted the 3x and got y X -2x=30000 am i correct so far? if so, i then divide the y to the right side but I don't know where to go after that.

bobbym · 2010-05-16 16:32:26

Hi;

I got for a finished product (3y - 30000) / 3 = x = f '(y)

alz921 · 2010-05-16 16:35:25

How did you get that? i dont know how that could work with a 3 in the numerator and in the denominator.

bobbym · 2010-05-16 16:37:11

Same page a little way down you will see the heading solve using algebra, please read that again.

alz921 · 2010-05-16 16:38:51

Yes that is what i did. Maybe im moving over the wrong thing first. what did you move first. did you multiply the x over?

bobbym · 2010-05-16 16:44:56

Hold on, we have a problem!

alz921 · 2010-05-16 16:46:44

alright.

bobbym · 2010-05-16 16:54:47

Hi;

Let's try this:

alz921 · 2010-05-16 16:56:16

Thank you for the help bobby. i appreciate it a lot. I am getting off now and will be checking this in the morning before going to class. still not sure how you found the inverse you did but ill look at it again and try it out but could you put your steps down so i know how to find it.

alz921 · 2010-05-16 16:57:12

haha alright thanks. i didnt think about that at all wow i feel dumb. that makes sense to me now.

bobbym · 2010-05-16 16:57:33

Hi;

You just solve for x and when you have done that replace x with y and y with x. Glad to help!

Math Is Fun Forum

#1 2010-05-16 15:13:56

Rational Function Help

#2 2010-05-16 15:29:24

Re: Rational Function Help

#3 2010-05-16 15:38:11

Re: Rational Function Help

#4 2010-05-16 15:43:26

Re: Rational Function Help

#5 2010-05-16 15:49:17

Re: Rational Function Help

#6 2010-05-16 15:52:29

Re: Rational Function Help

#7 2010-05-16 15:56:51

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#8 2010-05-16 16:05:16

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#9 2010-05-16 16:06:32

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#10 2010-05-16 16:08:54

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#11 2010-05-16 16:10:31

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#12 2010-05-16 16:15:21

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#13 2010-05-16 16:25:06

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#14 2010-05-16 16:32:26

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#15 2010-05-16 16:35:25

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#16 2010-05-16 16:37:11

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