Q$.4$ Three products $A,B$ and C are produced at three machine centers X $,$

Y and Z $.$ Each products involves operation at each of the machine centers.

The time required for each operation on various products is indicated in

the following table

a$)$ Formulate a linear programming problem on the basis of above

information.

b$)$ Find out the product mix so as to maximize profit by simplex method.

c$)$ Show that the total available hours of $x$ and $Y$ have been fully utilized and

there is surplus hours of Z $.$ How many hours are surplus in machine

center Z$?$