new boyofshit

21. If the value of a decision variable is zero at the optimal solution, its reduced cost is

(b) the amount its objective function value would need to improve before it could become positive

company uses 4 pounds of resource 1 to make each unit of x1a nd 3 pounds of resource 1 to make each unit of x2. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between x1,x2 and resource 1?

4x1+ 3x2<150

24. Which of the following actions should expand the feasible region of an LP model?

a. Loosening the constraints

. In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables

a. TRUE

2. What are the three common elements of an optimization problem?

b. Decision variables, constraints, an objective

32. A constraint that does not affect the feasible region is a .

b. redundant constraint

33. All linear programming problems have all of the following properties EXCEPT .

c. alternative optimal solutions

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is given by .

c. range of optimality

12. Linear programming problems have

d. linear objective functions, linear constraints

In sensitivity analysis, a zero shadow price for a resource ordinarily means that the resource has not been used up.

true

Which one of the following can be an objective function?

x1+x2+x3+x4

19. Which one of the following statements is NOT true?

(c) An infeasible solution violates all constraints.

. The constraint for a resource is 5x1 + 4x2 ≤ 200. If x1 = 20, what is the maximum value x2 can take on?

25

3. What is the main goal in optimization problems?

Find the values of the decision variables that satisfy all constraints and maximize/minimize the value of the objective function

25. When do alternate optimal solutions occur in LP models?

a. When a constraint is parallel to an objective function line

22. The constraints of an LP model define the

a. feasible region

1. Mathematical programming is referred to as

a. optimization

26. A redundant constraint .

a. plays no role in determining the feasible region of the problem

A set of values for the decision variables that satisfy all the constraints and yields the highest/lowest objective function values is.

an optimal solution

15. The third step in formulating a linear programming problem is to

b. state the constraints as linear combinations of the decision variables

A manager has only 200 tons of plastic for his company. This is an example of a(n

constraint

Limited resources are modeled in optimization problems as

constraints

14. The second step in formulating an LP problem is to

d. state the objective function as a linear combination of the decision variables

The lettersx1,x2,x3, etc. are all examples of.

decision variable

23. If constraints are added to an LP model, the feasible region will generally .

decrease

The graphical method of solving linear programming models can handle only maximization problems.

false

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality

false

13. The first step in formulating an LP problem is to

identify the decision variables

20. All of the following statements about a redundant constraint are correct EXCEPT

it the optimal solution, a redundant constraint will have zero slack

The desire to maximize profits is an example of a(n

objective

The improvement in the value of the objective function per unit increase in the right-hand side value of a constraint is the .

shadow price

Regarding the types of points in a feasible region, an extreme point is a corner point and it is also a boundary point.

true

When integer variables are present, the solution time can increase dramatically and no sensitivity output is generated.

true

For a linear programming problem, we observe that a given resource has not been fully used at the optimal solution. We can conclude that the shadow price associated with that constraint

value of zero

A production optimization problem has 4 decision variables and a resource limits how many of the 4 products can be produced. Which of the following constraints can reflect this fact

x1 + x2 + x3 < 120

For a resource constraint, either its slack value must beor its shadow price must be

zero zero