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A print shop uses exactly 150 reams of paper each day of the

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A print shop uses exactly 150 reams of paper each day of the [#permalink] New post 14 Jul 2006, 06:00
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A print shop uses exactly 150 reams of paper each day of the calendar year. If it orders the paper at least once every four days, it can store the paper in the existing storage space. Alternatively, the shop can place larger, less frequent orders and rent extra storage space. The table above details the prices for ordering paper from its supplier. Currently, the print shop orders paper every day. Would this print shop save money if it ordered paper once a month instead?

(1) The annual cost of renting extra storage space for a month’s supply of paper is $2,000.
(2) The regular price of 5000 reams of paper is the same as the annual cost of renting extra storage space for a month’s supply of paper.
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Re: DS: Print shop [#permalink] New post 14 Jul 2006, 06:44
Let the total price for the paper that the shop uses be x (without discount).
So currently on a daily basis, the shop has to pay
95% of X (price after discount)+ $10*365 (delivery charge)
= 95%of X + 3650 ---------------- 1

Consider (1), the monthly need will be 4500 reams
Using this the total cost would be
= 85%of X + $100*12 + 2000
= 85%of X + 3200 --------------------2

Comparing this with the first eq, the amount for a monthly order will be less than daily order.
So (1) is enough to say if the print shop would save money.

Consider (2), this just says that the monthly cost of order and renting space are the same,
That means if the total cost is 85%of X, monthly cost will be around 85%of X/12 ~= 7%of X
So total cost is
= 85%of X + 1200 + 7%of X
= 92%of X + 1200 ------------------3

3 is state that monthly cost will be greater.

So in all, both (1) and (2) alone are sufficient.

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kevincan wrote:
A print shop uses exactly 150 reams of paper each day of the calendar year. If it orders the paper at least once every four days, it can store the paper in the existing storage space. Alternatively, the shop can place larger, less frequent orders and rent extra storage space. The table above details the prices for ordering paper from its supplier. Currently, the print shop orders paper every day. Would this print shop save money if it ordered paper once a month instead?

(1) The annual cost of renting extra storage space for a month’s supply of paper is $2,000.
(2) The regular price of 5000 reams of paper is the same as the annual cost of renting extra storage space for a month’s supply of paper.
Re: DS: Print shop   [#permalink] 14 Jul 2006, 06:44
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