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#1 2007-01-31 02:09:52

jxharmon
Member
Registered: 2007-01-08
Posts: 104

HELP please....Business & Finance

An inventor of a new product believes that the cost of producing the product is given by the function C(x) = 1.75x + 7000.

If the inventor charges $4 per unit, then her profit for producing and selling x units is given by the function P(x) = 2.25x - 7000

a) What is her profit if she sells 2000 units?
b) What is her profit if she sells 5000 units?
c) What is the break-even point for sales?

How do I work a,b, and c?

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#2 2007-01-31 02:26:27

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: HELP please....Business & Finance

Since the function of profit is given as P(x), what you need to do are only evaluate it in corresponding points and solve x when P(x)=0.


X'(y-Xβ)=0

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#3 2007-01-31 04:03:16

jxharmon
Member
Registered: 2007-01-08
Posts: 104

Re: HELP please....Business & Finance

can you do one of a, b, or c for an example...please

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#4 2007-01-31 05:19:50

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: HELP please....Business & Finance

As you wish.

For a, she's selling 2000 units, so her profit it given by 2.25*2000 - 7000. This works out to be -2500, so she's making a considerable loss.

b is exactly the same, but you're substituting x = 5000 instead of 2000.

c is slightly different, but not too much harder. There, you just need to solve the equation 2.25x - 7000 = 0.


Why did the vector cross the road?
It wanted to be normal.

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#5 2007-01-31 05:41:23

jxharmon
Member
Registered: 2007-01-08
Posts: 104

Re: HELP please....Business & Finance

U R Awesome, Thxs!

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#6 2007-02-01 03:56:36

jxharmon
Member
Registered: 2007-01-08
Posts: 104

Re: HELP please....Business & Finance

OK...can you double check me?

a) -2,500
b) 4,250
c) not sure but here is how I worked it:

2.25x-7000=0
+7000          +7000
2.25x=-7,000/2.25
      x= -3,111

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#7 2007-02-01 06:33:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: HELP please....Business & Finance

You're nearly right. You just need to get rid of that minus sign that crept in there.
Also, the step where you said that 2.25x = 7000/2.25 is wrong.
I know what you meant, but you can't have that 2.25 on both sides at once like that.


Why did the vector cross the road?
It wanted to be normal.

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#8 2007-02-01 08:37:20

jxharmon
Member
Registered: 2007-01-08
Posts: 104

Re: HELP please....Business & Finance

Got it, thanks.

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