Q$4.$ a$)$ A company produces $2$ products A and $B$ which requires raw materials $400$ units and $450$ labour hours. It is known that $1$ unit of product A requires $5$ units of raw materials $10$ labour hours to yield a profit of $$45.$Product $B$ requires $20$ units of raw materials and $15$ man hours to yield a profit of $ $80.$

Required:Formulate the Linear Programming problem model

b$)$ A firm produces three products A$,$B and C$.$The profits are $$3$$$2$ and $$4$ respectively. The firm has two machines and below is given the required processing time in minutes foe each machine on each product.

$\backslash$table$[[,$PRODUCTS,PRODUCTS,PRODUCTS$],[$MACHINE$,A,B,C$