Download Linear Programming Problem: Solving a System of Equations using Simplex Method and more Exams Operational Research in PDF only on Docsity! Eg q3\2' oTeca'h-r^-s P"e€*'l'- E J{,\\ "lrof 3. (28 points: 10+5+3+5+5) In the middle of sdlving an LP problem, a tableau looked as follows: P-\o'Q- x L t/r L ,ly The objective function of the LP is maxz : atrr * atrc where both'gr and. 0r are positivej All the parts are independent of each other ,^ / iU),;S"ppose s : 0.-Does this LP have a unique optimal solution? If yes, then why? If no, then fi.nd t ( "r =ffy three oesal sotuli'J:i \a.\a 4 r-r,ii1'.r th.^^\ s{\t"^ bcco.*e- ^ ,,^r-\+(\r- von*Hc (*) Vv^\ ".- coe-(t''cir^\ aQ o \: .:*, " iti* Ui*r- -\ | z I2 L4 rs R]IS I 0 a 0 0 1 4 0 0 3 I 0 I 0 0 I 0 I 2 0 1 2 n 0 2 I \0 -,f - I (a) As a warm up, write the current basic variables, non-basic variables, their values and the -- /objective function value. Suppose ihe original LP had three ( constraints with RHS being,l,2 and I respectively. Then what is the number of decision variagl/.x in the original LP? !-ti.c *.;-H.*s t x' = I, x s= I' xy = Zyr/$taa (onU.ir_ vas*b\r.t'" f z =O. Xs =o obr.-c\'.r, S*,ND- ? ."'a^1 aae,ft''*O'(o\ = e' 6'' }\t> c''x- Q't9'it) rh = * a"^$-u\s *r\ o - ,r\ raAAAos +" u.'o J' *J'q St "irl\ rni^\Ls n ! rb *..4^\lr,l h ?f\ bo.jtc s \.fto^s -n - w\ -- L 3\nrJ- 2 *^t'"N,. a'{- 6.^!rs}< C=^"\ i s}nu'' v'.. =3 '"t "f ,/ ;T -.:;' ir"*'- "'\ ll'- us\4*' "b^a \: a j\r*\ ' ( olr..:" \.* 3r"'^'^ l^ B\\S B! 'BAb )a,= | t.l=L Xr=O x.. =O ,Yo= I t -.{ *\"* t'll''tt" €.,b\-c,. {Z ',-34-X \^' x L \o' (t*' I K I xL I(r l\7-\? 2) xr xl Xr toxr'i rs 'o L:1 I 3 .-! I =$ Lut"---*-ffi- o ? (c) Determine the value of d1. \ "' ?-lt [o-\ ,u.r- r : e, (r\ * e'tq =9t ThL .r a\'{ tq a \k= 1r:^\ \= t{ , *o (d) Suppose e, : -1, then what is the optimal solution? qN'^\ oo1$\o* :lo oo oD o\ \^l\u.\ .lc*\\.-,., tx o \ o o o B/n o - t/q. | 'o/r o '"/r x, ='/' ). " t t/s Ig ='b lt 's/3 xs =o a = tt/s 7s 2 '/ z 001 1D-ls oll DOL I z ^*,r.{=L X, = \ o o o I f ,2 I o o o tls Ys -r/s -'/s r3/g '/s as '/s Xztth xr -tA Y, ='/ | /\ ^i (e) .Suppose now that o : 1. If the column below 15 looked as follows: l1l llll_11 l_rl | _i I instead of l, ft | (* it looks right now) then what can you say about the feasible region l-zl lzl of LP and the optimal solution? Answer is less than 50 words. \.\ -\s *,.;, :*,.;i+' |t*"- F-;\A ' L"- "^Lo"+Lr;31{^'v\ !r-1. +L o?\;\t lffS*\"S:\''( L \'*\r' +D A\l: I do**' ' s\'^ X\ xs. ^r\ jr='b..n- J r\a i: t+l$* J x"= x' ' = x\ =s \'^ to '^r o \ t'r'-. ." *^'-t *\'\* '*tl'^ '*- \ lf,.o, =r\'h'^ t =L\ \: '\\\^t^\ a ^* \\.- sr*q\J. .{-"\f,".I ^''\ Ar*'o-' ,9 F u,r-".-bo ,,J-L-)
