The maximum value of z = 9 x + 13 y subject to constraints 2 x + 3 y ≤ 18 , 2 x + y ≤ 10 , x ≥ 0 , y ≥ 0 is

Step-by-step solution

Given, constraints are 2 x + 3 y ≤ 18 , 2 x + y ≤ 10 , x ≥ 0 , y ≥ 0 . The feasible region is O A B C O . Also, z = 9 x + 13 y At O ( 0 , 0 ) , z = 0 At A ( 5 , 0 ) , z = 45 At B ( 3 , 4 ) , z = 27 + 52 = 79 At C ( 0 , 6 ) , z = 78 ∴ Maximum value of z is 79 .