The minimum value of Z = 3x + y , subject to the constraints 2x + 3y 6, x + y 1, x 0, y 0 is....

Step-by-step solution

The objective function is Z = 3x + y . The given constraints are: 2x + 3y 6 x + y 1 x 0, y 0 The feasible region is bounded by the lines 2x + 3y = 6 , x + y = 1 , x = 0 , and y = 0 . The corner points of the feasible region are the intersections of these lines with the coordinate axes: For x + y = 1 , the intercepts are (1, 0) and (0, 1) . For 2x + 3y = 6 , the intercepts are (3, 0) and (0, 2) . Thus, the vertices of the feasible region are (1, 0) , (3, 0) , (0, 2) , and (0, 1) . Evaluating Z = 3x + y at each corne