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mixture problem

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mixture problem [#permalink] New post 16 Nov 2010, 15:50
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A
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Difficulty:

  55% (hard)

Question Stats:

63% (02:46) correct 37% (02:52) wrong based on 19 sessions
A company produces 450 units of a particular computer component every month, at a production cost to the company of $110 per component, and sells all of the components by the end of each month. What is the minimum selling price per component that will guarantee that the yearly profit (revenue from sales minus production costs) will be at least $626,400 ?

a)226 b)230 c)240 d)260 e)280
[Reveal] Spoiler: OA

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Re: mixture problem [#permalink] New post 16 Nov 2010, 15:56
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I pick "A"


You need to set up an equation.

450*12(x-110)=626400

where x is a selling cost of one item
x-110, is a profit from one item

450 - number of items produced and sold per month
12 - is a number of month in a year

Simplifying the equation will lead to x-110=116, then x = 226
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Re: mixture problem [#permalink] New post 18 Nov 2010, 15:56
simple but time consuming...

incurring profit 626400 is equal to incur profit 52200 per month.

total production cost = 450*110= 49500
Total selling price = 49500+52200=101700

Thus price per equipment= 101700/450 = 226

Answer:- A
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Re: mixture problem [#permalink] New post 22 Nov 2010, 18:29
Expert's post
Sarang wrote:
simple but time consuming...

incurring profit 626400 is equal to incur profit 52200 per month.

total production cost = 450*110= 49500
Total selling price = 49500+52200=101700

Thus price per equipment= 101700/450 = 226

Answer:- A


Hey Sarang,
That's the trick of GMAT. For many questions, there is a long calculation approach and a short cut.
Selling price per item = 110 + \(\frac{626400}{(12*450)}\)
Considering that all options are integers, you know you will end up canceling everything out to obtain 110 + 116 = 226
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Re: mixture problem   [#permalink] 22 Nov 2010, 18:29
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