UTK Math 123 Exam 3 True/False

In a feasible basic solution all the variables (with the possible exception of the objective) are nonnegative.

True

If, at any stage of an iteration of the simplex method, it is not possible to compute the ratios (division by zero) or the ratios are all negative, then the standard linear programming problem has no solution.

True

In a feasible basic solution all the variables (with the possible exception of the objective) are positive.

False

The graph of a linear inequality consists of a line and some points on both sides of the line.

False

In the final tableau of a simplex method problem, if the problem has a solution, the last column will contain no negative numbers.

False

Some linear programming problems have more than one solution.

True

Every minimization linear programming problem can be converted into a standard maximization linear programming problem.

False

The solution set of the inequality 2x + 6y ≤ 12 is on and below the line 2x + 6y = 12.

True

In the final tableau of a simplex method problem, if the problem has a solution, the last column will contain no negative numbers above the bottom row.

True

Choosing the pivot column by requiring that it be the column associated with the most negative entry to the left of the vertical line in the last row of the simplex tableau ensures that the iteration will result in the greatest increase, or, at worst, no decrease in the objective function.

True

In a standard maximization linear programming problem, each constraint inequality may be written so that it is less than or equal to a nonnegative number.

True

The feasible region of a linear programming problem with two unknowns may be bounded or unbounded.

True

Some linear programming problems have exactly two solutions.

False

Choosing the pivot row by requiring that the ratio associated with that row be the smallest non-negative number ensures that the iteration will not take us from a feasible point to a non-feasible point.

True

Every linear programming problem in two unknowns has optimal solutions.

False

Every minimization problem can be converted into a maximization problem.

True

A linear programming problem with an unbounded feasible region never has a solution.

False

If a linear programming problem has a solution at all, it will have a solution at some corner point of the feasible region.

True

The simplex method can be used to solve all linear programming problems that have solutions.

True

In the simplex method, a basic solution can assign the value zero to some active (or basic) variables.

True

The solution set of 2x - 3y < 0 is below the line 2x - 3y = 0.

False

The following is a standard maximum linear programming problem:

Maximize p = -2x - 3y - Z subject to

4x - 3y + z ≤ 3

-x - y - z ≤ 10

2x + y - z ≤ 10

x ≥ 0, y ≥ 0, z ≥ 0

True

The following is a standard maximum linear programming problem:

Maximize p = x - y - 3z subject to

4x - 3y - z ≤ -3

x + y + z ≤ 10

2x + y - z ≤ 10

x ≥ 0, y ≥ 0, z ≥ 0

False

The following linear programming problem has an unbounded feasible region:

Minimize c = x - y subject to

4x - 3y ≥ 0

3x - 4y ≤ 0

x ≥ 0, y ≥ 0

True

The following linear programming problem has an unbounded feasible region:

Minimize c = x - y subject to

4x - 3y ≤ 0

3x - 4y ≥ 0

x≥ 0, y ≥ 0

False