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March 31st, 2008, 01:54 PM   #1
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Upper lower bounds

unladen, a lorry weighs 2.3 tonnes, measured to the nearest 100kg. the lorry is loaded with crates, each weighing 250kg, correct to the nearest 10kg. On its journey the lorry crosses a brdige with a maximum safe load of 15 tonnes. what is the maximum number of crates that the driver can load onto the lorry?

its an upper and lower bounds question.

the answer in the book says 49, but I dont quite understand how you get there. i thought you would use the lower bound on lorry and the lower bound of the crates so that you can have more crates, but the text book obviously diagrees.

can somebody explain how to get to 49 and what it is that i'm doing wrong?
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March 31st, 2008, 02:46 PM   #2
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Re: Upper lower bounds

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Originally Posted by Kiranpreet
unladen, a lorry weighs 2.3 tonnes, measured to the nearest 100kg. the lorry is loaded with crates, each weighing 250kg, correct to the nearest 10kg. On its journey the lorry crosses a brdige with a maximum safe load of 15 tonnes. what is the maximum number of crates that the driver can load onto the lorry?

its an upper and lower bounds question.

the answer in the book says 49, but I dont quite understand how you get there. i thought you would use the lower bound on lorry and the lower bound of the crates so that you can have more crates, but the text book obviously diagrees.

can somebody explain how to get to 49 and what it is that i'm doing wrong?
I didn't do the arithmentic. However in order to insure safety in crossing the bridge, you have to use the upper bound on the weight for the crates, not the lower bound. Also add in the safety factor for the lorry.
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March 31st, 2008, 04:06 PM   #3
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Re: Upper lower bounds

Quote:
Originally Posted by Kiranpreet
i thought you would use the lower bound on lorry and the lower bound of the crates so that you can have more crates, but the text book obviously diagrees.
Using the lower bounds and rounding the number of crates up ensures that you have enough to break the bridge. Using the upper bounds and rounding the number of crates down ensures you won't break the bridge. It's all about what you want to do.

However, when I work out the problem I get only 48 crates. I wonder where your book got 49?
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March 31st, 2008, 11:42 PM   #4
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thanks for the help, i reckon the book is wrong
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April 1st, 2008, 10:42 AM   #5
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The book also seems to assume that the driver fully loads the lorry before driving it across the bridge, but there's nothing in the question to prevent him from fully loading it only after crossing the bridge.
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