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A microprocessor plant that manufactures computer chips costs $\$400,000$ per day to operate. It costs $\$30$ to produce one chip which sell for $\$190$ dollars. How many chips does the plant have to make to break even on one day operation?

Let $X$ be the number of chips I need to make.

$400,000 = 190X-30X$ (but I'm not sure this is even right). I'll continue anyway, I'll check it later...

$400000 = 160X$

$X=2500\quad$ ?

$2500 * 190 = 475000$ (its wrong)

Can someone help me? I think that formula I have is very wrong and I can't figure out another one...

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  • $\begingroup$ 2500 is the answer. It is not wrong. Please explain clearly why you think it is wrong. (See Gadi A's comments below.) $\endgroup$ – ShreevatsaR May 22 '11 at 10:25
  • $\begingroup$ You should calculate number of chips*(selling price per chip - manufacturing cost per chip) to get 400 000. In this case you have just calculated number of chips*selling price per chip. So, what is $2500 \times (190-30)$? $\endgroup$ – Calle May 22 '11 at 14:00
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You seem to have the correct answer (definitely the correct method to solve this). Why do you think "2500 * 190 = 475000" means you are wrong? Remember that the number of chips also takes into account their manufacture cost.

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  • $\begingroup$ When you check the problem it has to be 400000 not 75000 more, that's where I'm lost. $\endgroup$ – Liger86 May 22 '11 at 8:46
  • $\begingroup$ Why? Try to elaborate. $\endgroup$ – Gadi A May 22 '11 at 8:53
  • $\begingroup$ I made this problem up to help me solve similar problems, the original problem has multiple choice answers where the solution works out to exactly break even on one day of operation. $\endgroup$ – Liger86 May 22 '11 at 8:59
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    $\begingroup$ I still don't understand why you consider the solution wrong. There is no sense in expecting 400*190 to come out 400000, since what you are trying to "break even" here is the total costs against the total revenues, and the total cost is larger than 400000. $\endgroup$ – Gadi A May 22 '11 at 9:24
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Your method of checking the answer is incorrect. $2500\cdot 190=475000$ is the total gross income from producing 2500 chips, but the cost of producing those 2500 chips is not just 400000, but $400000+2500\cdot 30=475000$, since each of the 2500 chips costs \$30 to produce.

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