Question

Solve the linear programming problem graphically. Minimize c= 2x–5y, subject to (x+ y = 10 {3x – y 26 (x20, y20 (3x + y = 5 Use the simplex method to maximize p = 2x + y, subject to {x+2y 2 . x>0, y20

both questions require different ways of solving.

Answer 1

Given that, Minimize o = 22-5y subject to, x+y=10 3a-Y 7,6 x7,0, y> 0 step-I: consider, x+y=10 lo O step-II: Consider, 3re-y=6 - (2) de - 6 step- Add o f. 4 = 16 => [@=41 i from ② ly=61 Hence, (4,6) is point of intersection. step-IV! Consider, graph as follows. 38-y=6. 10 ploio) VCC4,6) S ET B (2,0) -5 ACoo) S 10 X rty=10 -10

step II As optimal solution lies at corner points. - 2x-5%. At A CO,O): دوره \C 5210)-500)=0 6) At B (2,0) B1 (20) = 2020-5log = 4 L (4) At C(4,6) = 2645-5(6)=8-30=-22 cl (4,6) L (5) ATD (0,10) Dlco, lo = 2(o)-5c1o) = -50 from (3), (4), (5) & (6) C has minimum at point (0,10). 14.once soin is. x=0, y=10