Expert: Frederick Koh - 12/23/2011

Question
A glass manufacturing company uses two types of raw materials (type A sand and type B sand) to produce three products (optical glass, bottle glass and window glass). Demand placed upon each product is as follows: 15 dozens of optical glass, 20 dozens of bottle glass, and 25 dozens of window glass. The unit cost of converting the raw materials to the various products is:
$12 to convert type A sand to optical glass
$3 to convert type A sand to bottle glass
$5 to convert type A sand to window glass
$8 to convert type B sand to optical glass
$2 to convert type B sand to bottle glass
$4 to convert type B sand to window glass
Formulate a linear programming model for the problem.
Use the North West Corner to find the initial cost of the problem.

Answer
If you wish to employ the north west corner method, certain information is missing from your given question, namely the number of glass products supplied by the two types of sands A, and B. For your convenience let them represent a and y respectively.


Abbreviations: OG-optical glass , BG-bottle glass,  WG-window glass

Quantities demanded for OG, BG and WG are 150*12=180, 20*12=240 and 25*12=300 respectively.


The Matrix is given below:



                  OG        BG        WG

Type A         12         3         5          x
         
         
Type B         8          2          4          y
         

              180         240        300       720



Note that we can't proceed without knowing what x and y are.


PS: This question is upper college stuff related to operations research. Kindly pose this in the relevant section in future. Thanks. Peace.