Problem Statement: An operations manager is trying to determine a production plan for the next week. There are three products $($say$,P,Q,$ and $R)$ to produce using four machines $($say$,$ A and B$,$ C$,$ and D$).$ Each of the four machines performs a unique process. There is one machine of each type, and each machine is available for $2400$ minutes per week. The unit processing times for each machine is given in the machine data table below:

Machine Data:

$\backslash$table$[[$Unit Processing Time $($min$)],[$Machine$,$Product P$,$Product Q$,$Product R$,$Availability $($min$)],[$A$,20,10,10,2400],[$B$,12,28,16,2400],[$C$,15,6,16,2400],[$D$,10,15,-,2400],[$Total Processing Time,$57,59,42,9600]]$

The unit revenues and maximum sales for the week are indicated in the product data table below. Storage from one week to the next is not permitted. The operating expenses associated with the plant are $$6000$ per week, regardless of how many components and products are made. The $$6000$ includes all expenses except for material costs.

Product Data:

$\backslash$table$[[$Item$,$Product $P,$Product $Q,$Product $R$