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 August 2nd, 2010, 10:08 PM #1 Newbie   Joined: Aug 2010 Posts: 1 Thanks: 0 How do I calculate this? I have a question for you guys: I have 5 buckets: Bucket A can only fit 100 apples Bucket B can only fit 50 apples Bucket C can only fit 75 apples Bucket D can only fit 100 apples During the day I want to fill each bucket as apples comes in. At the end of the day each bucket should be filled equally base on the max allowed. So if Bucket A got 75% filled then Bucket B, C, and D should also be filled at 75% or close to 75% What is a good formula to use for that? Also please note that Bucket B or D would not be available in the morning only in the afternoon.
August 7th, 2010, 10:20 AM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

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Re: How do I calculate this?

Hello, "KM_!

We need a [color=red]lot[/color] of clarification!

Quote:
 I have 5 buckets: [color=beige]. . [/color]$\begin{array}{c|c} \text{Bucket} & \;\;\text{Capacity} \\ \hline \\ \\ A & 100 \\ \\ \\ B & 50 \\ \\ \\ C & 75 \\ \\ \\ D & 100 \end{array}$ During the day I want to fill each bucket as apples comes in. [color=blue]I assume that this means: we put the first 100 apples into Bucket A.[/color] [color=beige]. . [/color][color=blue]then put the next 50 apples into Bucket B,[/color] [color=beige]. . [/color][color=blue]and so on . . .[/color] At the end of the day each bucket should be filled equally based on the max allowed. [color=blue]Now sure what this means.[/color] So if Bucket A got 75% filled then Bucket B, C, and D should also be filled at 75% or close to 75%[color=blue] Why would we stop filling Bucket A at 75% ? [/color] What is a good formula to use for that? [color=blue]Formula for what?[/color] Also please note that Bucket B or D would not be available in the morning only in the afternoon. [color=blue]Does this mean that buckets A and C are filled in the morning[/color] [color=beige]. . [/color][color=blue]and only buckets B and D are filled in the afternoon?[/color]

I have an interpretation of the problem which makes the above procedure rather silly.

[color=beige]. . [/color]$\begin{array}{ccc} \text{Bucket} & \;\;\text{Capacity}\;\; & \text{Fraction} \\ \hline \\ \\ A & 100 & \frac{100}{325} \:=\:\frac{4}{13} \\ \\ \\ C & 75 & \frac{75}{325}\:=\:\frac{3}{13}\\ \\ \\ B & 50 & \frac{50}{325} \:=\:\frac{2}{13}\\ \\ \\ D & 100 & \frac{100}{325} \:=\:\frac{4}{13} \\ \\ \\ \hline \\ \text{Total:} & 325
\end{array}$

Suppose 260 apples were harvested.

Then the buckets are filled in order and we would have:

[color=beige]. . [/color]$\begin{array}{c|c} \text{Bucket} & \text{apples} \\ \hline \\ \\ A & 100 \\ \\ \\ C & 75 \\ \\ \\ B & 50 \\ \\ \\ D & 35 \\ \\ \hline \\ \\ \text{Total:} & 260\end{array}$

Now that we know that 260 apples were harvested,
[color=beige]. . [/color]we can go back and redistribute the apples.

[color=beige]. . [/color]$\begin{array}{c|c|c} \text{Buckets} & & \text{Apples} \\ \hline \\ \\ A & \frac{4}{13}\,\times\,260 & 80 \\ \\ \\ C & \frac{3}{13}\,\times\,260 & 60 \\ \\ \\ B & \frac{2}{13}\,\times\,260 & 40 \\ \\ \\ D & \frac{4}{13}\,\times\,260 & 80 \\ \hline \end{array}$

So that each bucket is filled to 80% of its capacity.

Is that what you're looking for?

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