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Quick solution?

by awilhelm » Fri Jan 30, 2009 7:47 am
A certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months from November through October?

a) .40x
b) 1.20x
c) 1.40x
d) 1.60x
e) 3.20x

I plugged in numbers to solve, but there must be a faster way...
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by DanaJ » Fri Jan 30, 2009 8:35 am
I'm not sure this is the correct way to solve it, buy here goes: you get total production of 4x (4 months nov through feb) until March. Now they start selling the stuff. Since they sell x/2 rakes every month, this means that between March and oct they sell the whole stock (since you've got 8 months: March through oct). Now the storage costs follow a certain pattern. For March they pay storage for 4x - x/2 = 7x/2 rakes, then for April they pay storage for 7x/2 - x/2 = 6x/2 = 3x, and so on, until they pay storage for only x/2 in Sept. So the amount of money they spent on storage will be:
7x/2 + 6x/2 + 5x/2 + 4x/2 + 3x/2 + 2x/2 + x/2 = x/2(1 + 2 + ... + 7)= x/2 * (7+1)*7/2 = 1.4x.

Answer: C
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by masuarezdl » Fri Jan 30, 2009 9:23 am
DanaJ wrote:I'm not sure this is the correct way to solve it, buy here goes: you get total production of 4x (4 months nov through feb) until March. Now they start selling the stuff. Since they sell x/2 rakes every month, this means that between March and oct they sell the whole stock (since you've got 8 months: March through oct). Now the storage costs follow a certain pattern. For March they pay storage for 4x - x/2 = 7x/2 rakes, then for April they pay storage for 7x/2 - x/2 = 6x/2 = 3x, and so on, until they pay storage for only x/2 in Sept. So the amount of money they spent on storage will be:
7x/2 + 6x/2 + 5x/2 + 4x/2 + 3x/2 + 2x/2 + x/2 = x/2(1 + 2 + ... + 7)= x/2 * (7+1)*7/2 = 1.4x.

Answer: C
Dana, I had a slightly different approach at the end. Can you help me out and tell me if this is correct?

From November - February: 4 months
From March to October: 8 months
Therefore, starting on March, we must substract

4x - x/2 = 8x/2 - x/2 = 7x/2, then for every month...

7x/2 + 6x/2 + 5x/2 + 4x/2 + 3x/2 + 2x/2 + x/2 = 28x/2 = 14x

Then, 14x at $0.10 per rack, is 1.4x.

Is this approach correct?
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by DanaJ » Fri Jan 30, 2009 11:12 am
Sure is... It's basically the same as mine...
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by ajmoney09 » Fri Jan 30, 2009 11:50 am
I am trying to plug in numbers to get this and i plug in 100 for X which gives me 400 rakes....50 rakes per month are delivered my cost is 50 bucks per month over 8 months gives me 40 bucks...

which gives me A....where am i going wrong?

whats the OA?
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by DanaJ » Fri Jan 30, 2009 11:55 am
ajmoney09: you are forgetting smth. And that is that each month x/2, in your case 50 rakes, are delivered. But remember that you had an initial stock of 400. That means that, since you deliver 50 rakes in March, you will pay storage for 400 - 50 = 350. In April, the situation changes: you deliver 50 rakes at the very beginning of the month, but you are left with 350 (left from last month) - 50 = 300 rakes for which to pay storage. And so on until September... Hope you understand where your mistake is: you don't pay storage for x/2 (in you case 50) every month, but you pay storage for the remaining stock after having sold 50 at the beginning of the month.
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by ajmoney09 » Fri Jan 30, 2009 11:57 am
DanaJ wrote:ajmoney09: you are forgetting smth. And that is that each month x/2, in your case 50 rakes, are delivered. But remember that you had an initial stock of 400. That means that, since you deliver 50 rakes in March, you will pay storage for 400 - 50 = 350. In April, the situation changes: you deliver 50 rakes at the very beginning of the month, but you are left with 350 (left from last month) - 50 = 300 rakes for which to pay storage. And so on until September... Hope you understand where your mistake is: you don't pay storage for x/2 (in you case 50) every month, but you pay storage for the remaining stock after having sold 50 at the beginning of the month.
Wow. Okay yuh that would mess up the numbers....Okay thanks so much.
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