申論題

1. (25 points) Enjoy the beauty of the simplex method. Let us solve the following linear programming problem by the simplex method without tabular forms. (Please DO NOT use tabular forms to solve it.)
  

(a) (5 points) Let us introduce the slack variables x₃, x₄, x₅, x₆ to constraints 1, 2, 3, and 4, respectively so X1,1220 that the objective function and equations, which are called dictionary, can be written as

We let x₃,x₄,x₅,X₆ in the above dictionary be basic variables, and x₁and x₂ be the nonbasic variables. What is the initial feasible solution (x₁, X₂,X₃,X₄.X₅, X₆.Z) based on the above dictionary in (a) if both nonbasic variables are set as zero?