# A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 35 per package of nuts and Rs14 per package of bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates each machine for atmost 12 hours a day ? Convert it into an LPP and solve graphically.

To maximize : $Z= Rs\left ( 35x+14y \right )$
subject to constracts: $x\geq 0,y\geq 0$
$x+3y\leq 12,3x+y\leq 12$
B(3,3)                                            14 $\leftarrow$ maximum