The feasible region for the inequations x+2 y 4,2 x+y 6, x, y 0 is

Step-by-step solution

The given system of linear inequalities is x + 2y 4 , 2x + y 6 , x 0 , and y 0 . First, consider the boundary lines: 1. x + 2y = 4 : This line passes through (0, 2) and (4, 0) . 2. 2x + y = 6 : This line passes through (0, 6) and (3, 0) . Next, determine the intersection point of the two lines: From x + 2y = 4 , we have x = 4 - 2y . Substituting into 2x + y = 6 : 2(4 - 2y) + y = 6 8 - 4y + y = 6 -3y = -2 y = 2 3 . Then x = 4 - 2( 2 3 ) = 4 - 4 3 = 8 3 . The intersection point is ( 8 3 , 2 3 ) . Now, analyze the reg