Question

10. For the following linear programming problem, determine the optimal solution by the graphical solution method. Are any of the constraints redundant? If yes, then identify the constraint that is redundant. Max x + 2y s.t. x + y<= 3 x - 2y >=0 y<= 1 x, y >= 0

Please show all work in excel and step by step with formulas no solvers mode.

Answer 1

Page No:1 Given: Max z = x + 2y nty < 3 x-24 > 0 o y <1, ?, Y>,0 To draw constraints at y <3 x+y = 3 when x=0 Y = 3 When yoo x - 3 у 3 9 o 3

Page No: 2 To draw constraint x - 2y > 0 2-2y0 when x = 0 y=o when y=0 x=0 a L2 o To draw constraint constraint yst ... y = 1 Here line is parallel to x-axis x 1 1 y ܝܙ

Page No: 3 The value of the objective function at each of the extreme point is Extreme Point Lines through coordinates (2,4) extreme point 2 = x+2y x-2y < 0 100)+200)=0 xzo objective function O(0,0) Á (2,1) 1 (2) + 211)=4 x+yL3 x-2y7, o B (3,0) x+y <3 1 (3) +210)=3 o Z = 4 occurs The maximum value of the objective function at the extreme point (2, 1) :: The optimal solution to the given LP problem is : p=2 y = 1 max Z=4