3.4 EXERCISES In Exercises 1-5 the given tableau represents a solution to a linear programming pr...
3. (2 points) The tableau r421 21 02 5 3 2 10 1 6 4 2 1 0 0 0 represents a solution to the linear programming problem Minimize z 41 22 + r3, subject to the constraints 31 +2a2+r3 6, that satisfies the optimality criterion but is infeasible. Use the dual simplex method to restore feasiblity and hence find an optimal solution.
The final simplex tableau for the linear programming problem is below. Give the solution to the problem and to its dual. Maximize 6x+ 3y subject to the constraints 5x+ ys 60 3x+ 2y s 50 x20, y20 x 1 0 4 0 10 0 10 1 90 For the primal problem the maximum value of M 11 which is attained for xD yL For the dual problem the minimum value of M is , which is attained for u-L Enter...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
The initial tableau of a linear programming problem is given. Use the simplex method to solve it. X1 X2 x3 S1 S2 z 1-0여 8 3 8 1 0 110 -3 -24 1 0 0 0
Linear Programming Problems 1. Write the basic feasible solution from the tableau given here. 5 0 -3 1 6 0 0154 8 1 5 0 14 0 086 -2 0 1 0 8 1 039 Linear Programming Problems 1. Write the basic feasible solution from the tableau given here. 5 0 -3 1 6 0 0154 8 1 5 0 14 0 086 -2 0 1 0 8 1 039
Based on this linear programming problem below, and answer the following questions: Minimize subject to Z=500 y, + 200 y, 3y, + y 24 -y, +2y, 210 y; - y, 215 -y, +4y, 225 y, 20, y, 20 and 1) Find the dual to the linear programming problem. 2) Using the simplex method to solve the dual problem. 3) The simplex method in part 2) should require 3 pivots (4 tableaus including the initial one). For each tableau, write the...
Consider the following linear programming problem Manimize $45X1 + $10X2 Subject To 15X1 + 5X2 2 1000 Constraint A 20X1 + 4X2 > 1200 Constraint B X1, X2 20 Constraint C if A and B are the two binding constraints. a) What is the range of optimality of the objective function? 3 C1/C2 s 5 b) Suppose that the unit revenues for X1 and X2 are changed to $100 and $15, respectively. Will the current optimum remain the same? NO...
This is the initial tableau of a linear programming problem. Solve by the simplex method. S1 S3 X1 1 2 S2 0 1 X2 3 4 2 N OOO 12 4 1 0 1 0 0 0 1 0 0 - 2 - 1 0 The maximum is when X1 = O, x2 =D Sy = 10, s2 = 0, and s3 = 2.
The following simplex tableau is in final form. Find the basic feasible solution to the linear programming problem associated with this tableau. 12 y 24 WP Constant 0 1/2 0 1 -1/2 0 0 To 1/4 1 0 5/4 -1/2 0 11 1 1/4 0 0 -3/4 1/2 0 LO 13 0 0 4 1/2 1
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...