The minimum value of Z=3 x+5 y , given subject to the constraints x+y 2, x+3 y 3, x, y 0 is

Step-by-step solution

The objective function is Z = 3x + 5y . The constraints are x + y 2 , x + 3y 3 , x 0 , and y 0 . To find the feasible region, determine the intersection points of the boundary lines: 1. x + y = 2 passes through (2, 0) and (0, 2) . 2. x + 3y = 3 passes through (3, 0) and (0, 1) . The intersection of x + y = 2 and x + 3y = 3 is found by subtracting the equations: (x + 3y) - (x + y) = 3 - 2 2y = 1 y = 0.5 . Substituting y = 0.5 into x + y = 2 , we get x = 1.5 . The intersection point is (1.5, 0.5) . The vertices of th