The total man$-$hour available for the processes are: $($A$,60$ hr$),($B$,44$ hr$)$ and $($C$,18$ hr$).$

The market research team in the company dictates that at most $($no more than$)10$ standard slabs of X$2$

type could be produced over the coming period.

$($i$)$ Tabulate the data;

$($ii$)$ Develop a linear programming model that will enable the company to maximize its profit;

$($iii$)$ Find the optimal solution using graphical method,

$($iv$)$ Find the optimal solution if the profits were: $1$ $$/$slab type $1$ and $3$ $$/$slab type $2$