A company manufactures $3$ products: X$,$ Y and Z$.$ The sales demand and the standard

unit price and costs for the next accounting period $1$ are estimated below;

X Y Z

Maximum Demand $($units$)4,0005,5007,000$

Selling price $($Rs$.)2,8002,2003,000$

Raw Materials $($Rs$\mathrm{.}100$ per Kg$)500400600$

Direct Labour $($Rs$\mathrm{.}1,200$ per hour$)1,2009001,800$

a$)$ If supplies in period $1$ are restricted to $90,000$ Kg of raw materials and $18,000$ hours of

direct labour hours, what would be the limiting factor?

$(06$ marks$)$

b$)$ In period $2,$ the company will have a shortage of raw materials, but no other resources

will be restricted. The standard selling prices and costs and the level of demand will

remain unchanged. Find the profit$-$maximizing materials allocation.