The maximum value of x+y subject to 2 x+3 y 6, x 0, y 0 is

Step-by-step solution

The objective function is Z = x + y . The constraints are 2x + 3y 6 , x 0 , and y 0 . The feasible region is a triangle with vertices at the origin (0, 0) , the x-intercept of the line 2x + 3y = 6 which is (3, 0) , and the y-intercept of the line 2x + 3y = 6 which is (0, 2) . We evaluate the objective function Z = x + y at the vertices of the feasible region: At (0, 0) : Z = 0 + 0 = 0 At (3, 0) : Z = 3 + 0 = 3 At (0, 2) : Z = 0 + 2 = 2 Comparing the values 0, 3, 2 , the maximum value is 3 . Answer: 3