2. Consider the LP maximize subject to 7.0 2.0 0 3.0 +8.02 +22 < 5 +2.r2...
Duality Theory : Consider the following LP problem: Maximize Z = 2x1 + x2 - x3 subject to 2x1 + x2+ x3 ≤ 8 4x1 +x2 - x3 ≤ 10 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Find the dual for this LP (b) Graphically solve the dual of this LP. And interpret the economic meaning of the optimal solution of the dual. (c) Use complementary slackness property to solve the max problem (the primal problem). Clearly...
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
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...
5. Waner p 302 #1) Given the LP problem: Maximize p = 2x + y subject to: Constraint 1: x + 2y <= 6 Constraint 2: -x + y<=4 Constraint 3: x + y = 4 XX. >= 0 The final simplex tableau is as follows: Basic 10 0 Answer the following questions: Find the new value of the objective function when b3 is changed from 4 to 6. g) The range of values of 4 (63) such that the...
Problem 3 Consider the LP problem Minimize -3r22 0s1+0s2 +0s3 0s Subject to 228 2r2 + $2 1,2,81,82 8384 with optimal tableau as follows: sic r1 T2 s1 s2 s3 s4 Solution C 0 0 20 1 0 0 12 Optimum 0 30 0-103 4 0 021 2 Find the dual optimal solution and the corresponding objective function value using the information provided in the optimal simplex tableau. Problem 3 Consider the LP problem Minimize -3r22 0s1+0s2 +0s3 0s Subject...
Consider the following LP problem. minimize 3:01 +4.c3 subject to 2:01 + x3 - I3 < -2 21 +3.02 – 5x3 = 7 21 <0,22 > 0, 03 free Which of the LP problem below is its dual problem? maximize -2p1 + 7p2 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4 Vi < 0,2 > 0 maximize --2p1 + 702 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4...
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+...
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
please answer all the question and explain clearly! THANKS! Exercise 6 Consider the LP problem subject to 1 1/2 T2 S1 2 2. 1, 0. After applying the Simplex method, the last simplex tableau is the follow- ng: z x1 x2 81 82 83|RHS -1 0 0 0 0 1-2 1 0 1 0 1 01/2 82 0 2 10 r20 0 1 201 Explain if the problem has one solution, infinitely many, or none. If it has infinitely many...
(5) Consider the problem: minimize I[r(.)] - /r2 dt 0 subject to the conditions x(0)-x()-0 and the constraint 0 R is a C2 function that solves the above Suppose that x : [0, π] Let y : [0, π] → R be any other C2 function such that y(0) = Define problem y(n) 0. 0 an a(s) a. Explain why α(0)-1 and i'(0) b. Show that 0. i'(0)r'(t) y'(t) dt -X /x(t) y(t) dt 0 0 for some constant λ,...