# Quantitative Methods: True/False

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7. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints' prices.

8. The sensitivity range for an objective coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

9. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

10. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

11. The solution value (Z) to the linear programming relaxation of a maximization problem will always be less than or equal to the optimal solution value (Z) of the integer programming maximization problem

12. The solution to the LP relaxation of a maximization integer linear program provides a lower bound for the value of the objective function.

13. If we are solving a 0-1 integer programming problem, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint.

14. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

15. The transshipment model is an extension of the transportation model in which intermediate transshipment points are added between the sources and destinations.

FILL IN THE BLANKS

16. An ______________ solution violates at least one of the model constraints.

17. Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.

18. The sensitivity range for an _____________coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

19. In a maximization linear programming problem profit is maximized in the objective function by subtracting cost from ____________.

20. In a problem involving capital budgeting applications, the 0-1 variables designate the ____________ or _____________ of the different projects.

21. In solving an integer linear programming problem, rounding ____ ________ solution values does not guarantee neither an optimal nor a feasible solution.

22. If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________________constraint.

23. An example of a ________________ point is a distribution center or warehouse located between plants and stores.

24. A plant has 4 jobs to be assigned to 4 machines, each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of 4 jobs to 4 machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________________ model.

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Response:

7. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints' prices.

- True: When conditions of change in right hand side of constraints are satisfied (100% rule) the value of objective function will be adjusted by sum of constraints' prices (dual prices)

8. The sensitivity range for an objective coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal.

- True: The basis remains same (optimal solution point or product mix remains same). Any change in objective function coefficient value within the range will change the objective function value, but not the optimal product mix.

9. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

- True: Because supply is equal to demand, total supply will be equal to total demand. In a balanced transportation model all constraints are treated as equality.

10. In a mixed ...

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