Shade the feasible region for the inequations x+y 2,2 x+3 y 6, x 0, y 0 in a rough figure.

Step-by-step solution

The given system of linear inequations is x + y 2 , 2x + 3y 6 , x 0 , and y 0 . First, consider the boundary lines: 1. x + y = 2 : This line passes through (2, 0) and (0, 2) . The region x + y 2 lies on or above this line. 2. 2x + 3y = 6 : This line passes through (3, 0) and (0, 2) . The region 2x + 3y 6 lies on or below this line. The intersection point of the two lines x + y = 2 and 2x + 3y = 6 is found by solving the system: 2(2 - y) + 3y = 6 4 - 2y + 3y = 6 y = 2 . Substituting y = 2 into x + y = 2 , we get x =