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# Linear programming problem

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You need to organize your home office, especially your paperwork. You have three general kinds of paperwork: tax files, bill files, investment files. You estimate that you have 10 tax files, 30 bill files, and 15 investment files. Each month you access each tax file three times; each bill file, two times; and each investment file, eight times. You have three places to put files, a file cabinet, your desk, or a storage box. The file cabinet can hold 30 files; the desk, 10 files; and the storage box, 25 files. When a file is accessed, the time it takes for a file to be accessed depends on the type of file and where you put it. You need to decide where to put your files. Your goal is to minimize the total time you spending each month accessing your files.

Retrieval Time (minutes)

(See attached)

Hint: The minimum retrieval time will be 660 minutes per month.

## SOLUTION This solution is FREE courtesy of BrainMass!

Let Xij = No of i files stored in j storage space where i=t, b, i and j=f, d, s
For example, Xtf = No of tac files stored in file cabinate.

Decision variables
Tax Files Bill Files Investment Files
File Cabinet xtf xbf xif
Desk xtd xbd xid
Storage Box xts xbs xis

Formulation:
Minimize Z= 3*(5xtf+3xtd+10xts) + 2*(3xbf +2xbd +6xbs) + 8*(4xif +1xid +8xis)
S.t. constraints

xtf +xtd +xts = 10
xbf +xbd +xbs =30
xif +xid +xis = 15
xtf + xbf +xif <= 30
xtd + xbd +xid <= 10
xts + xbs +xis<= 25
xij >=0

Solution in attached excel file.

Tax Files Bill Files Investment Files
File Cabinet 10 15 5
Desk 0 0 10
Storage Box 0 15 0

By solving the problem using Excel solver, we get following results:
Store 10 tax files in file cabinet, 15 Bill files in file cabinet, 15 Bill files in storage box, 5 Investment files in file cabinet, and 10 investment files in Desk with minimum total retrieval time of 660 minutes/month.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!