You are using the simplex method to solve the following linear programming problem.Maximize Z = 6x₁ + 5x₂ - x₃ + 4x₄,subject to 3x₁ + 2x₂ - 3x₃ + x₄ ≤ 120 3x₁ + 3x₂ + x₃ + 3x₄ ≤ 180 and x₁ ≥ 0,x₂ ≥ 0,x₃ ≥ 0,x₄ ≥ 0.You have obtained the following final simplex tableau where x₅ and x₆ are the slack variables for the respective constraints. Use the fundamental insight presented in Sec.5.3 of the textbook to identify Z*, ,and .

Question

Quizplus · Accepted Answer

The Answer is The fundamental insight presented in Sec.5.3 of the textbook states in part that Z* =y*b,

= S*b,where y* =

is the vector of coefficients of the slack variables in Eq.(0),S* =

is the matrix of coefficients of the slack variables in the remaining equations,and b is the vector of the original right-hand sides.(Since S = B^-1,where B is the basis matrix,and y* = c_BB^-1,where c_B is the vector of the objective function coefficients of the basic variables,this alternative notation may be used throughout this solution.)Therefore,the final right-hand side is

= S* b =

=

,and Z^* = y*b =

= 315.

You Are Using the Simplex Method to Solve the Following