True/False Quiz for Chapter 4

Linear Programming

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

2. The graph of a linear inequality consists of a line and only some of the points on one side of the line. True False

3. The graph of a linear inequality consists of a line and all of the points on one side of the line. True False

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

5. No point other than a corner of the feasible region can be a solution to an LP problem. True False

6. No point in the interior of the feasible region can be a solution to an LP problem. True False

7. Every LP problem has a solution. True False

8. Every LP problem with a bounded nonempty feasible region has a solution. True False

9. No LP problem with an unbounded feasible region has a solution. True False

10. The graphical method is practical for all LP problems. True False

11. The simplex method can be used to solve all LP problems. True False

12. Constraints can always be turned into equations by adding slack variables to the left-hand sides. True False

13. Constraints can always be turned into equations by subtracting surplus variables from the left-hand sides. True False

14. Constraints can always be turned into equations by adding or subtracting slack or surplus variables from the left-hand sides as appropriate. True False

15. To minimize c you can instead maximize p = -c. True False

16. In a basic solution some of the variables are 0. True False

17. The variables that are 0 are those that appear on the left. True False

18. In a feasible basic solution all the variables are nonnegative. True False

19. When all of the numbers in the bottom row are nonnegative you are done with the simplex method. True False

20. When all the variables (with the possible exception of the objective) are nonnegative and all the numbers in the bottom row are nonnegative (with the possible exception of the rightmost) you are done with the simplex method. True False