$[$Q$3]$: Suppose that you are the production engineer in Basra oil company and want to find the optimal number of mixing operations of two blending processes.

The following data are given: $($Formulate the LPP only$)$

$\backslash$table$[[$Process$,$Input $($Crude Oil$),$Output $($Gasoline$)],[$Grade A$,$Grade B$,$X$,$Y$],[$P$1,6,4,6,9],[$P$2,5,6,5,5]]$

Profit per operation for P $1$ is $4000$$$,$ while for P $2$ is $5000$$$.$ Maximum availability of crude oil of Grade A is $500$ units, while for Grade B is $400$ units. Minimum Demand for Gasoline of type X is $300$ units, while for Y is $200$ units. $(7$Marks$)$