Question

6. Consider the equation ſi 0 -17 |x=b, x>0. [1 1 1 Find all the basic feasible solutions x for these values of b: []: [] [] 67 (-2): [ - ] [-] Draw a picture of the set of all b if x is feasible.

Answer 1

+ Almost basic solution of a system Aman Xon=bma is no * A soluton x of Amin Xnxi= b is said to be is feachtë if X30 k 1:(X1, D20 14 01320; VI-lyn (11) basic if it is obtain by pulling nominuariables af x to zero Cand soluing remaining lyttem). (1) for b = (%) = ax=b! Chot')(%= 11 • Almost basic. foluhon = ?ca= . This pult X₂=0 and soluing remaining lystem we get ball Holuhun B=(2,-2,0) + o buroudly B, Nul bali fearble CBFS) clue to 2270 pult X=0 8 " we get: Be = (1, 0,-1) - obuioulley B20 Not BFS. S duo to Xco full s4=0 f solving r. system : B3 = (0, 2,-) --) obuoly B3 ( Not BFS (21 for b=(}) =) Ax=b: (1 7 )=(} ) • pult 3,20 in abou & soluing remaining system B, = 0,6,-3) - Oburowily Bior nof BFS due to Xco . pult >=0 . . Bz = (5,0., 0) + Itu BES became 40; 42433) i pult (3=0 & . . . By: (3,0,0) - Itix BES O- X . ) b=(2) =) Axsb: .. pult Na=o in above & soleing remaining tudtem = B= (3,3,0) + BFS berale XX O .. pult 2-0 . . . By: %0,3) + BES . pull Y=o . . .. - B = (0,9,-3) 'Not BFS duto foco Similarly we can do this for next values of ble