Question

362 Chapter 9 nteger Linear Programming 9-56. Develop the B&B tree for each of the following problems. For coaseni xi as the branching variable at node 0. (a) Maximizez 3xi + 2r2 subject to x, x2 2 0 and integer (b) Maximizez2r, + 3x2 subject to 5x 7x2 s 35 x1, x2 0 and integer (c) Maximizezx + x2 subject to 2x1 + 5x2 s 16 6x 5x2 s 27 x1, x2 0 and integer (d) Minimize z = 5x1 + 4x2 subject to 3x1 2x2 2 5 2x1 + 3x2 2 7 x1, X2 2 0and integer (e) Maximizez 5x 7x2 subject to 2x1 + x2 s 13 5x1 + 9x2 41 xi, x2 2 0 and integer

USE THE BRANCH AND BOUND (B&B) ALGORITHM!!!!

Please show all the steps, including the branching and the graphs.

Answer 1

Assignment ( 2.15. o), o Co. o), . A 2oo2) 16 : 10125 Xi : I. 6875、 C2 7:312 ....a ding...Censivan 6.S o b-B 군 : 6 2,

Ye ra. Lon aximum va

SOLUTION Maximize 2: 2지+3x2 S4bject to 2 o and integev SoLUTIor his pvoblem can be solved thvough simplex method So. The e augmented matvix Covve sponling to tnis maai mization Pvoblem) is 36 2. 3 us the matvix Covvesponding to the dlual mini mization Pvoblem is given by -the follouwing tvanspose 2 3 36 This implies that dual min Oual minimization Pvoblem find the minimum Nalue oh dual obiective fancticlual Constvaints imi zation pvoblem is as folloos

Subjeck to Consivaints dual Constvaints Wheve y, zo, 20 and Yz ue now apply the simplex mcthod to the dual pvoblem as ollows -35-36 Entevinq block Aftev Solving pivot table 니 1 O Basic Non - Uasi c

Do the itovation 0 -The solution ot dual pvoblem is-, sla "yiz, 2s P-9