2. (20 pts.) Find the optimal s method lex olution for the following LP problem using the appropriate simp (Hint: DO NO...
Use the Big M method to find the optimal solution to the following LP: min z = -3x1 + x2 s.t. X1 - 2x2 2 -x1 + x2 3 x1, x2 0 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. Use the Big M method to find the optimal solution to the following LP: Max z = 5x1 − x2 s.t.: 2x1 + x2 = 6 x1 + x2 ≤ 4 x1 + 2x2 ≤ 5 x1, x2 ≥ 0 Answer: z = 15, x1 = 3, x2 = 0.
please help! Use the Big M method to find the optimal solution to the following LP: max z = x1 + x2 s.t. 2x1 + x2 > 3 3x1 + x2 = 3.5 x1 + x2 = 1 X1, X2 = 0
I need help on the knapsack lp by using branch and bound ) Use the branch-and-bound method to find the optimal solution to the ollowing IP: Minimize 9x1 +13x2 +10x3 +8x4 +8x5 s.t.6x1+3x2+2x3+4x4+7x5240 X131,x221,x322,x421,x5s3 X1, X2, X3, X4, X5 20 integer ) Use the branch-and-bound method to find the optimal solution to the ollowing IP: Minimize 9x1 +13x2 +10x3 +8x4 +8x5 s.t.6x1+3x2+2x3+4x4+7x5240 X131,x221,x322,x421,x5s3 X1, X2, X3, X4, X5 20 integer
2. Solve the following LP problem using the simplex method s.t. - 3Xl- X22-6 X1 +X224 and Xl 2 0,X2 u.r.s. HINT: Use the Big-M Method to find an initial bfs.
(a) State the dual problem. (b) Solve both the primal and the dual problem with any method that works. (c) Check that your optimal solutions are correct by verifying they are feasible and the primal and dual objective functions give the same value. 9. Minimize z subject to 4x1 + x2 + x3 + 3x4 2x, + x2 + 3x3 + x4 2 12 3xi + 2x2 + 4x3 2x1-x2 + 2x3 + 3x4-8 3x1 + 4x2 + 3x3 х,2...
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this problem without using the simplex algorithm, but using the fact that an optimal solution to LP exists at one of the basic feasible solutions.
Problem 3. (a) Solve the following LP problem using the Simplex Method. Use the smallest- subscript rule to choose entering and leaving variables. Show all steps. maximize xi+ 5.02 + 5x3 + 524 subject to X1+ 412 + 3x3 + 3x4 < 17 12 + x3 + x4 <4 Xit 202 + 2x3 + 3x4 < 10 X1, ..., 84>0. (b) Is the optimal solution you found the only one? Explain.
Problem 3. Solve the following LP by the simplex method. max -x1 + x2 + 2xz s. t x1 + 2x2 – x3 = 20 -2x1 + 4x2 + 2x3 = 60 2xy + 3x2 + x3 = 50 X1, X2, X3 > 0 You can start from any extreme point (or BFS) that you like. Indicate the initial extreme point (or BFS) at which you start in the beginning of your answer. (30 points)
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25 Problem 1 (20 pts) Consider...