Example: An operations manager is trying to determine a production plan for the next week. There are three products $($say$,$ P$,$ Q$,$ and Q$)$ 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 Table $1.$

$\backslash$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$,10,15,0,2400],[$Total processing time,$57,59,42,9600]]$

Table $1$: Machine Data

The unit revenues and maximum sales for the week are indicated in Table $2.$ 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.

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