The maximum value of P=500 x+400 y for the given constraints x+y 200, x 20, y 4 x, y 0 is

Step-by-step solution

The constraints are given as: 1) x + y 200 2) x 20 3) y 4x 4) y 0 The feasible region is determined by the intersection of these lines. We find the vertices of the feasible region: Intersection of x = 20 and y = 4x : x = 20 , y = 4(20) = 80 . Vertex: (20, 80) . Intersection of x + y = 200 and y = 4x : x + 4x = 200 5x = 200 x = 40 . y = 4(40) = 160 . Vertex: (40, 160) . Intersection of x + y = 200 and x = 20 : 20 + y = 200 y = 180 . Vertex: (20, 180) . We evaluate the objective function P = 500x + 400y at these vert