Question 1.(20 points): For each LP problem below, write down the dual LP problem associated with...
Q3. (Dual Simplex Method) (2 marks) Use the dual Simplex method to solve the following LP model: max z= 2x1 +4x2 +9x3 x1 x2 x3 S 1 -x1+ X2 +2x3 S -4 x2+ X1,X2,X3 S 0 Q3. (Dual Simplex Method) (2 marks) Use the dual Simplex method to solve the following LP model: max z= 2x1 +4x2 +9x3 x1 x2 x3 S 1 -x1+ X2 +2x3 S -4 x2+ X1,X2,X3 S 0
Write down the associated dual problem. (ii)Given the information that the optimal basic variables are 1xand 3x, determine the associated optimal dual solution (1y, 2y and w). Maximize subject to z = x, +5x2 + 3x3 x, + x2 + x3 = 3 2x, - x2 = 4 *,,X, X, 20 (i) Write down the associated dual problem. (5 marks) (ii) Given the information that the optimal basic variables are x, and xz, determine the associated optimal dual solution (y,,...
Consider the following LP problem max z = x1 +2x2 + x3 + x4 s.t. x1 + 2x2 + x3 く2 +2x3 く! X1, x2, x3, x4 20 a) Obtain the dual formulation of the LP.
please explain it to me clearly 6 Proof of the dual theorem Proof: We will assume that the primal LP is in canonical form Maximize Zr, such that Arb 20 12 Its dual is Minimize W·ry, such that ATy c (no sign constraints on y). Step 1: Suppose xB is the basic variables in the optimal BFS (say r*) f follows from the above discussion that Row (0) of the optimal tableau will be the Prianal LP. It Basic VariableRow2...
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
2a. Consider the following problem. Maximize 17-Gri +80 Subject to 5x1 + 2x2 320 i 212 10 and Construct the dual problem for the above primal problem solve both the primal problem and the dual problem graphically. Identify the corner- point feasible (CPF) solutions and comer-point infeasible solutions for both problems. Calculate the objective function values for all these values. Identify the optimal solution for Z. I 피 University 2b. For each of the following linear programming models write down...
using the simplex method. In Problems below, each maximum problem is not in standard form. Determine if the problem can be modified so as to be in standard form. If it can, write the modified version. 11. Maximize 12. Maximize 13. Maximize P=x1 + x2 + x3 subject to the constraints subject to the constraints subject to the constraints 4x12x2 -8 3x1 4x2 -6 2 4 x1 + x2 + x3 6 4x1 + 3x2 12 x20 In Problems below,...
Please use the big M method to solve the following linear program. Write down all tableau, note basic variables and nonbasic variables. Use slack and artificial variables. Construct your tableau iterations using the standard form of the program. For example first line z+2x1-2x2+2x3=0. If possible, STATE THE OPTIMAL SOLUTION AND THE OPTIMAL VALUE. Otherwise state why you cannot find them. Consider the following linear program: 2x3 max z= –2x1 + s.t. + -x1 21 > 0, 2x2 - 2x2 +...
Question 2: Identify which of Cases (1)--(4) apply to the following LP problem. max z = 2x1 – X2 s. t. X1 – X2 < 1 2x1 + x2 > 6 X1, X2 > 0 (1) unbounded LP (2) infeasible LP (3) unique optimal solution (4) multiple optimal solutions
Question 11 (20 points) Let's essume the following LP model Provide the optimal values of the decision variables 0X1 and X2) and the optimal value of the objective function. Show your work as much as you can or send a picture of your work if you nane to get partial points when your final answers are not Objective function: Mim x, + X Operational constraints: X1 10: Xi 2.0 NonMgativityconstraints:x,-x, 20 Question 12 (20 paines) Let's assume the following LP...