I need help to solve problem 3-39* . Thank you so much!
124 Chapter 3 3-38. \"ii-39. "3-40. *541. 3-47.. The Simplex Method and Sensitivity Analysis Consider the following set of constraints: xr-t- 251+\": 7 Solve the problem fur each DI the [allowing tihjcctivi; ILtricLiuiis. (a) Maximize z : 2x, + 11; - 513. (h) Minimize z 7 2n + 3M 5rJ (c) Maximizez = In + 71'; + 13. (d) Minimiwez =4x, Riv: I in. Consider the problem Muximiu: z : 2n + 4x; + 4x; , 3A4 siihjacttu x1 17 + x, = 4 3174a +1.,i8 r1. X1, 7:3,)ri 2/: U Solve the prnhlem with x; and x; as the starting basic variables and Without using any a! Variables. (Him. x; and 51 play ll]: ml: of slack VariablesThe main diexence is that they have nonzero objective meicientn) Solve the following pi'oblerii using I; Lind X4 as starting basic taasiblc vanahlasl As in Problem 3739, (to not use any artificial variables. Minimize z = 3x1 " 2an + 3);; siihjecltu 11% 4x, wt; .2 7 bi + x! r1,x2.,r3,x, Considei the pioblem Maximizez 11 + 532 7 3X3 subject to x] + 2.x! + x; 7 3 2X. r2 = 4 x]: m, 2 0 The. variable r3 plays the role of a slack. lhi no articial variable is nDCdCLl iii the t'iist constraint. In thi; almond constraint, an artificial vnrinblu. R,is needed. Sulva the problem uaiiigx; and R as the smiling variables. Show Lliat Llie Mrinetliod will conclude that the following problem has no feasible snlutiou. Mn..:..:.. . _ m. I 1.. *3-43. 3 -44. 345. 3-46. 3-47. 54 Problems 125 subject in m Phasc I. if Ll'lL' LP in iii the maximization type explain why we do notmaximize the sum of the artificial vaiinbles in Pliuze I. For each case in Piobieui 337. Wl'lll.' lhc uurruspunding Pli it: I objective functinn, Solve PlOlJlEJ|13733JJy Lliu lwu-phasu muihud. Wiilc Phase I for the following piuhlcm, and thcn salve (Wllh TORA for convsnierlt'e) to show that the problem has no feasible solution. Maximizez , 2x, + 5 subject in in + 7x2 2 e m In K x2 5. .\\'|,X7 2 0 Considur lhu following [li'OhlElTlI Maximizez : 2x, i 2!; l 4):] subject to Li, + .i'2 13 8 \"11.x; a 0 (a) Show that Phase I will teimlnnte with an aitiiicial biii'i'c Vnilable at new level (you may use TOR A for convenience.) (b) Remow the LC\") artificial variahlc prior to the stari (1f Phase I I, then carry out Phase II iterations. Coitsidei the following pl'DlJlEl. Maximizaz , it, ~ 2!; + 31j siihjeci tn in 7 .xz + x; = 2 x1 I 1x2 i x;=( 3.\" l' 4x; I 2X; = R .rilxmx; T: 0 (a) Show thul Phaxc I turminates Vill'l twn 7.5m artificial variables in the haste solution (use TORA for convenience). (h) Show that whentl-ie procedure of Problem 3 47(1)) is applied at the end oi'Pliase I, nnllv \"r... ..r Hm Mun mm nm'minl run-"mm mm HA man mm Mm
