The minimum value of z = 3x + 5y , subject to constraints x 80 , y 60 , x + y 200 & x, y 0 occurs at the point...

Step-by-step solution

The given objective function is z = 3x + 5y . The constraints are x 80 , y 60 , x + y 200 , x 0 , and y 0 . The feasible region is a polygon bounded by the vertices (0, 60) , (80, 60) , (80, 120) , and (0, 200) . Evaluating the objective function z at each of these corner points: At (0, 60) , z = 3(0) + 5(60) = 300 At (80, 60) , z = 3(80) + 5(60) = 240 + 300 = 540 At (80, 120) , z = 3(80) + 5(120) = 240 + 600 = 840 At (0, 200) , z = 3(0) + 5(200) = 1000 The minimum value of z is 300 , which occurs at the point (0,