The point at which the maximum value of x + y subject to constraints x + 2y 70 and 2x + y 95, x 0, y 0 is.

Step-by-step solution

The objective function to be maximized is Z = x + y . The given constraints are: x + 2y 70 2x + y 95 x 0, y 0 The corner points of the feasible region are determined by the intersections of the boundary lines x + 2y = 70 , 2x + y = 95 , and the coordinate axes. Solving x + 2y = 70 and 2x + y = 95 : Multiplying the second equation by 2 gives 4x + 2y = 190 . Subtracting the first equation from this gives 3x = 120 x = 40 . Substituting x = 40 into x + 2y = 70 gives 40 + 2y = 70 2y = 30 y = 15 . The intersection point