Linear Programing Problem               Simplex Method

The GP Furniture Company makes and sells four models of loungs suites. The profits from these models are - 
      Standard $130, Special $180, Deluxe $240 and Emperor $350.

The manufacturing process consists of 5 sections -
     Cutting out the component parts
     Turning & Sanding
     Assembly
     Varnishing & Painting
     Padding & Covers.

An Emperor model takes 1,2,3,1,3 hours respectively to get through these sections. A Standard model takes an 
hour in each section except for Assembly where it only takes half an hour. The Special takes an hour each in 
Cutting out, Assembly and Padding, 2 hours in Turning & Sanding and 3 hours in Varnishing & Painting.  The 
Deluxe takes one and a half hours in Cutting out, 2 hours in Turning & Sanding, 4 hours in Assembly, 2 hours in 
Varnishing and one hour in Padding & Covers.

Only 9 tons (9000 kg) of wood is available to the factory each week and the models use the quantities of wood 
shown below for their construction.
       Standard  50kg     Special  100kg     Deluxe  150kg     and Emperor  100kg

The labour requirements for each section in the factory are limited to 
     Cutting out                  194 hours / week
     Assembly                    130 hours / week
     Turning & Sanding      184 hours / week
     Padding & Covers.       125 hours / week
    Varnish & Paint            200 hours / week



a) How many of each model should they make for maximum profit ?
b) What is the maximum profit that can be expected ?
c) Is there any slack in the factory ?
d) Are there any recomendations you would make to the company ?



Note:
There are computer programs that can do the Simplex method. Suitable software is available for downloading 
from the FTP site at the University of Tennessee. Select either the MAC or MSDOS section as appropriate.

     ftp://archives.math.utk.edu/software/

MAC’s          LinPro       in the directory         mac/discreteMath
MSDOS        Simplex      in the directory        msdos/discrete.math