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Math
Math exam 3 123 True False
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Terms in this set (20)
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 negative, then the standard linear programming problem has no solution.
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
Some linear programming problems have exactly two solutions.
False
Some linear programming problems have more than one solution.
True
The solution set of 2x - 3y < 0 is below the line 2x - 3y = 0.
False
In a feasible basic solution all the variables (with the possible exception of the objective) are nonnegative.
True
If a linear programming problem has a solution at all, it will have a solution at some corner of the feasible region.
True
Every minimization problem can be converted into a maximization problem.
True
Every minimization linear programming problem can be converted into a standard maximization linear programming problem.
False
Every linear programming problem in two unknowns has optimal solutions.
False
The simplex method can be used to solve all linear programming problems that have solutions.
True
Choosing the pivot row by requiring that the ratio associated with that row be the smallest non-negative number insures that the iteration will not take us from a feasible point to a non-feasible point.
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 feasible basic solution all the variables (with the possible exception of the objective) are positive.
False
In the simplex method, a basic solution can assign the value zero to some basic variables.
True
The feasible region of a linear programming problem with two unknowns may be bounded or unbounded.
True
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
A linear programming problem with an unbounded feasible region never has a solution.
False
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
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