The L.P.P. to maximize z=x+y , subject to x+y 30, x 15, y 20, x+y 15 , x, y 0 has

Step-by-step solution

array |l|l|l| line & Point on X-axis & Point on y-axis +y=30^ & A(30,0) & B(0,30) =15 & C(15,0) & - =20 & - & D(0,20) +y=15 & C(15,0) & F(0,15) array Point of intersection of x=15 and y=20 is E (15,20) Feasible region is FCEDF. We have to maximize Z=x+y array l Z_ (C) =15+0=15 Z_ (E) =15+20=35 Z_ (D) =0+20=20 Z_ (F) =0+15=15 array Thus minimum value 15 occurs at two vertices F and C . Thus given LPP has infinite solutions.