Note that is also binding at the current solution B B \u0153 53 5 a \u00e3 \u00e3 \u0153 \u00e3 \u00e3 D \u0153 \u00ca

# Note that is also binding at the current solution b b

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"#\$"#\$Note that is also binding at the current solution.#B  Bœ &!"\$5.3-5.(a)---ã!!ã!œ"#""!ã,#"\$!"ã#,!!D"#\$\$%(\$%&&"'&&- œÊ -œ-  # œ ! Ê -œ # -  \$ œ ! Ê -œ \$""##\$\$""(\$&"'#, , (b) , FœF, œ ,ÍœÍ , œ &\$Î&"Î&\$Î&"Î&,""Î&#Î&"Î&#Î&#,\$""(c) Using (a): ^œ - ,œœœ ""--#\$""\$\$F#\$Using (b): ^œ - , œœœ ""\$Î&%Î&\$Î&%Î&,&#,"!F
5-175.3-6.Iteration 1: Multiply row 2 by and add to row 0, i.e., premultiply by&Î#E!!&Î#!and add to row 0, where.Eœ"!ã"!!ã%!#ã!"!ã"#\$#ã!!"ã")!Iteration 2: Add row 3 to row 0, i.e., premultiply by and add to row 0,E!!""where.EœœE"!ã"!!ã%"!!!"ã!"Î#!ã'!"Î#!\$!ã!""ã'!"""!Therefore, the final row 0 is: initial row 0,E E!&Î#!!!"!"œE\$&ã!!!ã!!!"!"Î#!!!"!!!""&#!œE\$&ã!!!ã!!"\$#!5.3-7.(a) Use the columns corresponding to artificial variables in exactly the same way as aslack variable would have been used. Note that the shadow price of this column may bepositive or negative.(b) For the reversed inequalities, use the negative of the column corresponding to theslack variable in exactly the same formulae. The artificial column may be discarded.(c) Same as (b).(d) No change, use slack and artificial variables as above.
5-185.3-8.aximize Q^ œ*!B  (!B QB"#&subject to #B  B  Bœ #"#\$B  B B Bœ #"#%&B ß B ß B ß B ß B  !"#\$%&Initial Tableau:Coefficient ofBVEqRS^BBBBB^!"*!  Q(!  Q!Q!#QB"!#""!!#B#!#""#\$%&\$&!""#The columns that will contain for applying the fundamental insight in the final tableauWare those associated with and , since those columns form the identity matrixBB# ‚ #\$&in the initial tableau.5.3-9.(a) Fœ\$Î"!"Î"!#Î"!#Î&"Final constraint columns for :ÐB ß B ß B ß B ß B Ñ"#\$%'FE œœ\$Î"!"Î"!"%#"!!"\$Î&\$Î"!"Î"!#Î"!#Î&\$#!!""!#Î&#Î"!#Î&"-œ'Q  \$%Q  #FFinal objective coefficients for :ÐB ß B ß B ß B ß B Ñ"#\$%'- FE  - œ 'Q  \$%Q  #!"\$Î&\$Î"!"Î"!"!#Î&#Î"!#Î&F"œ%Q#'Q\$#Q#QQ!!""Î#"Î#Right-hand side:F, œœ)*Î&'%Î&"\$Î"!"Î"!#Î"!#Î&D œ "%Q  - Bœ "%Q œ (*Î&%Î&FF'Q  \$%Q  #
5-19Final tableau:(b) The constraints in the original tableau can be expressed as EãMãMã,with the second identity matrix corresponding to the artificial variables. Premultiply thismatrix by M to get:EãWãPã,EãMãMã,Eããã,œœM,MMMMwhere M.œ Wœ Pœ\$Î"!"Î"!