a) An …………………………... solution violates “at least one” constraint.

a) An ……………………………. solution is a feasible solution that provides “the most favorable” objective function value. (The largest for maximization and the smallest for minimization problems.)

a) A problem might have no optimal solution in the following two cases:

a) Assumer there is a total of n variables and m constraints in an LP model. Each variable can be either ………….…. variable or ……………... variable.

a) Number of basic variables always equals to the number of …………………………………….

a) Nonbasic variables are always set to …………………….

a) If a basic variable equals to zero in a final Simplex tableau, then the problem has a …………….….. optimal solution.

a) The problem is ...………………..……., if we cannot take a ratio test.

a) The problem is ...………………..……., if a final solution of Big-M or Phase I of Two-Phase method yields at least one artificial variable greater than zero.

a) If constraints have a less than equal to sign, …………………..…………………..…. variables should be used to apply the Simplex Method.

a) If constraints have a equal sign, …………………..…………………..…. variables should be used to apply the Simplex Method.

a) If constraints have a greater than equal to sign, …………………..…………………..…. variables should be used to apply the Simplex Method.

a) For a minimization problem where z = -3x₁ + 2x₂ – 5x₃, the corresponding maximization objective function in the standard form will be …………………………………………………………..…

a) In the Big-M Method, the starting tableau’s z^th row coeffients should be reorganized because the artificial variables will not satisfy the …………………….. form.