Quantitative Analysis for Management, 11e (Render)
Chapter 7 Linear Programming Models: Graphical and Computer Methods
1) Management resources that need control include machinery usage, labor volume, money spent, time used,
warehouse space used, and material usage.
2) In the term linear programming, the word programming comes from the phrase “computer programming.”
3) One of the assumptions of LP is “simultaneity.”
4) Any linear programming problem can be solved using the graphical solution procedure.
5) An LP formulation typically requires finding the maximum value of an objective while simultaneously
maximizing usage of the resource constraints.
6) There are no limitations on the number of constraints or variables that can be graphed to solve an LP problem.
7) Resource restrictions are called constraints.
8) One of the assumptions of LP is “proportionality.”
9) The set of solution points that satisfies all of a linear programming problem’s constraints simultaneously is
defined as the feasible region in graphical linear programming.
10) An objective function is necessary in a maximization problem but is not required in a minimization problem.
11) In some instances, an infeasible solution may be the optimum found by the corner point method.
12) The rationality assumption implies that solutions need not be in whole numbers (integers).
13) The solution to a linear programming problem must always lie on a constraint.
14) In a linear program, the constraints must be linear, but the objective function may be nonlinear.
15) Resource mix problems use LP to decide how much of each product to make, given a series of resource
restrictions.
16) The existence of non–negativity constraints in a two–variable linear program implies that we are always
working in the northwest quadrant of a graph.
17) In linear programming terminology, “dual price” and “sensitivity price” are synonyms.
18) Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility of multiple
solutions.
19) If the isoprofit line is not parallel to a constraint, then the solution must be unique.
20) When two or more constraints conflict with one another, we have a condition called unboundedness.
21) The addition of a redundant constraint lowers the isoprofit line.
22) Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at
a time.
23) A widely used mathematical programming technique designed to help managers and decision making
relative to resource allocation is called ________.
A) linear programming
B) computer programming
C) constraint programming
D) goal programming
E) None of the above
24) Typical resources of an organization include ________.
A) machinery usage
B) labor volume
C) warehouse space utilization
D) raw material usage
E) All of the above
25) Which of the following is not a property of all linear programming problems?
A) the presence of restrictions
B) optimization of some objective
C) a computer program
D) alternate courses of action to choose from
E) usage of only linear equations and inequalities
26) A feasible solution to a linear programming problem
A) must be a corner point of the feasible region.
B) must satisfy all of the problem’s constraints simultaneously.
C) need not satisfy all of the constraints, only the non–negativity constraints.
D) must give the maximum possible profit.
E) must give the minimum possible cost.
27) Infeasibility in a linear programming problem occurs when
A) there is an infinite solution.
B) a constraint is redundant.
C) more than one solution is optimal.
D) the feasible region is unbounded.
E) there is no solution that satisfies all the constraints given.
28) In a maximization problem, when one or more of the solution variables and the profit can be made infinitely
large without violating any constraints, the linear program has
A) an infeasible solution.
B) an unbounded solution.
C) a redundant constraint.
D) alternate optimal solutions.
E) None of the above
29) Which of the following is not a part of every linear programming problem formulation?
A) an objective function
B) a set of constraints
C) non–negativity constraints
D) a redundant constraint
E) maximization or minimization of a linear function
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
30) When appropriate, the optimal solution to a maximization linear programming problem can be found by
graphing the feasible region and
A) finding the profit at every corner point of the feasible region to see which one gives the highest value.
B) moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is
encountered.
C) locating the point that is highest on the graph.
D) None of the above
E) All of the above
31) The mathematical theory behind linear programming states that an optimal solution to any problem will lie at
a(n) ________ of the feasible region.
A) interior point or center
B) maximum point or minimum point
C) corner point or extreme point
D) interior point or extreme point
E) None of the above
32) Which of the following is not a property of linear programs?
A) one objective function
B) at least two separate feasible regions
C) alternative courses of action
D) one or more constraints
E) objective function and constraints are linear
33) The corner point solution method
A) will always provide one, and only one, optimum.
B) will yield different results from the isoprofit line solution method.
C) requires that the profit from all corners of the feasible region be compared.
D) requires that all corners created by all constraints be compared.
E) will not provide a solution at an intersection or corner where a non–negativity constraint is involved.
34) When a constraint line bounding a feasible region has the same slope as an isoprofit line,
A) there may be more than one optimum solution.
B) the problem involves redundancy.
C) an error has been made in the problem formulation.
D) a condition of infeasibility exists.
E) None of the above
35) The simultaneous equation method is
A) an alternative to the corner point method.
B) useful only in minimization methods.
C) an algebraic means for solving the intersection of two or more constraint equations.
D) useful only when more than two product variables exist in a product mix problem.
E) None of the above
36) Consider the following linear programming problem:
The maximum possible value for the objective function is
A) 360.
B) 480.
C) 1520.
D) 1560.
E) None of the above
37) Consider the following linear programming problem:
The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective
function?
A) 1032
B) 1200
C) 360
D) 1600
E) None of the above
38) Consider the following linear programming problem:
Which of the following points (X,Y) is not a feasible corner point?
A) (0,60)
B) (105,0)
C) (120,0)
D) (100,10)
E) None of the above
39) Consider the following linear programming problem:
Which of the following points (X,Y) is not feasible?
A) (50,40)
B) (20,50)
C) (60,30)
D) (90,10)
E) None of the above
40) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear
programming model is used to determine the production schedule. The formulation is as follows:
The optimal solution is X = 100, Y = 0.
How many units of the regular model would be produced based on this solution?
A) 0
B) 100
C) 50
D) 120
E) None of the above
41) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear
programming model is used to determine the production schedule. The formulation is as follows:
The optimal solution is X=100, Y=0.
Which of these constraints is redundant?
A) the first constraint
B) the second constraint
C) the third constraint
D) All of the above
E) None of the above
42) Consider the following linear programming problem:
What is the optimum solution to this problem (X,Y)?
A) (0,0)
B) (50,0)
C) (0,100)
D) (400,0)
E) None of the above
43) Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
44) Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
45) Which of the following is not acceptable as a constraint in a linear programming problem (maximization)?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) None of the above
46) If one changes the contribution rates in the objective function of an LP,
A) the feasible region will change.
B) the slope of the isoprofit or isocost line will change.
C) the optimal solution to the LP is sure to no longer be optimal.
D) All of the above
E) None of the above
47) Sensitivity analysis may also be called
A) postoptimality analysis.
B) parametric programming.
C) optimality analysis.
D) All of the above
E) None of the above
48) Sensitivity analyses are used to examine the effects of changes in
A) contribution rates for each variable.
B) technological coefficients.
C) available resources.
D) All of the above
E) None of the above
49) Which of the following is a basic assumption of linear programming?
A) The condition of uncertainty exists.
B) Independence exists for the activities.
C) Proportionality exists in the objective function and constraints.
D) Divisibility does not exist, allowing only integer solutions.
E) Solutions or variables may take values from –∞ to +∞.
50) The condition when there is no solution that satisfies all the constraints simultaneously is called
A) boundedness.
B) redundancy.
C) optimality.
D) dependency.
E) None of the above
51) If the addition of a constraint to a linear programming problem does not change the solution, the constraint is
said to be
A) unbounded.
B) non–negative.
C) infeasible.
D) redundant.
E) bounded.
52) Which of the following is not an assumption of LP?
A) simultaneity
B) certainty
C) proportionality
D) divisibility
E) additivity
53) The difference between the left–hand side and right–hand side of a less–than–or–equal–to constraint is referred
to as
A) surplus.
B) constraint.
C) slack.
D) shadow price.
E) None of the above
54) The difference between the left–hand side and right–hand side of a greater–than–or–equal–to constraint is
referred to as
A) surplus.
B) constraint.
C) slack.
D) shadow price.
E) None of the above
55) A constraint with zero slack or surplus is called a
A) nonbinding constraint.
B) resource constraint.
C) binding constraint.
D) nonlinear constraint.
E) linear constraint.
56) A constraint with positive slack or surplus is called a
A) nonbinding constraint.
B) resource constraint.
C) binding constraint.
D) nonlinear constraint.
E) linear constraint.
57) The increase in the objective function value that results from a one–unit increase in the right–hand side of that
constraint is called
A) surplus.
B) shadow price.
C) slack.
D) dual price.
E) None of the above
58) A straight line representing all non–negative combinations of X1 and X2 for a particular profit level is called
a(n)
A) constraint line.
B) objective line.
C) sensitivity line.
D) profit line.
E) isoprofit line.
59) In order for a linear programming problem to have a unique solution, the solution must exist
A) at the intersection of the non–negativity constraints.
B) at the intersection of a non–negativity constraint and a resource constraint.
C) at the intersection of the objective function and a constraint.
D) at the intersection of two or more constraints.
E) None of the above
60) In order for a linear programming problem to have multiple solutions, the solution must exist
A) at the intersection of the non–negativity constraints.
B) on a non–redundant constraint parallel to the objective function.
C) at the intersection of the objective function and a constraint.
D) at the intersection of three or more constraints.
E) None of the above
61) Consider the following linear programming problem:
The maximum possible value for the objective function is
A) 360.
B) 480.
C) 1520.
D) 1560.
E) None of the above
62) Consider the following linear programming problem:
Which of the following points (X,Y) is feasible?
A) (10,120)
B) (120,10)
C) (30,100)
D) (60,90)
E) None of the above