MGMT 3100
Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then
-.5A + .5B - .5C <= 0
Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is
0
Why might we not be able to build a regression model to predict a dependent variable?
All of these are true
Which of the following special cases does not require reformulation of the problem in order to obtain a solution?
Alternate optimality
Which of the following statements is NOT true?
An infeasible solution violates all constraints
All of the following statements about a redundant constraint are correct EXCEPT
At the optimal solution, a redundant constraint will have zero slack
Which of the following is not a question answered by sensitivity analysis?
By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?
Which of the following is not a quantitative technique for evaluating the accuracy of a time series modeling technique?
Constructing line graphs of the data
A company makes two products, A and B. A sells for $100 and B sells for $90. The variable production costs are $30 per unit for A and $25 for B. The company's objective could be written as: MAX 190x1 - 55x2.
False
A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input
False
A redundant constraint is a binding constraint.
False
Alternative optimal solutions occur when there is no feasible solution to the problem.
False
Any change to the objective function coefficient of a variable that is positive in the optimal solution will change the optimal solution.
False
Because surplus variables represent the amount by which the solution exceeds a minimum target, they are given positive coefficients in the objective function.
False
Decreasing the objective function coefficient of a variable to its lower limit will create a revised problem that is unbounded.
False
Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's.
False
Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.
False
The constraint 2x1 - x2 = 0 passes through the point (200,100).
False
The decision making process includes implementation and evaluation of the decision
False
The feasible solution is the best solution possible for a mathematical model
False
The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured
False
The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis
False
The volume that results in marginal revenue equaling marginal cost is called the break-even point
False
The volume that results in marginal revenue equaling marginal cost is called the break-even point.
False
To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.
False
Uncontrollable inputs are the decision variables for a model
False
Uncontrollable inputs are the decision variables for a model.
False
When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.
False
The determination of the MSE-minimizing value of the wi is a non-linear optimization problem because
MSE is a non-linear objective function
Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is
Min 2M + 3B
Which of the following is a valid objective function for a linear programming problem?
Min 4x + 3y + (2/3)z
To find the optimal solution to a linear programming problem using the graphical method
None of the alternatives is correct
A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There are 100 tons of steel available daily. A constraint on daily production could be written as: 2x1 + 3x2 <= 100.
True
A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective.
True
A range of optimality is applicable only if the other coefficient remains at its original value.
True
All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.
True
An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.
True
Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.
True
For any constraint, either its slack/surplus value must be zero or its dual price must be zero.
True
If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.
True
In a feasible problem, an equal-to constraint cannot be nonbinding.
True
In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.
True
In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.
True
Media selection problems can maximize exposure quality and use number of customers reached as a constraint, or maximize the number of customers reached and use exposure quality as a constraint.
True
Portfolio selection problems should acknowledge both risk and return.
True
Problem solving encompasses both the identification of a problem and the action to resolve it
True
Relevant costs should be reflected in the objective function, but sunk costs should not.
True
The constraint 5x1 - 2x2 £ 0 passes through the point (20, 50).
True
The first step in the decision making process is to identify the problem.
True
The most critical component in determining the success or failure of any quantitative approach to decision making is problem definition.
True
The point (3, 2) is feasible for the constraint 2x1 + 6x2 <= 30.
True
The process of decision making is more limited than that of problem solving
True
The reduced cost for a positive decision variable is 0.
True
The value of any model is that it enables the user to make inferences about the real situation
True
Which of the following is the common approach to time series analysis?
Try several techniques and use the best results
To solve a linear programming problem with thousands of variables and constraints
a personal computer can be used
All linear programming problems have all of the following properties EXCEPT
alternative optimal solution
A physical model that does not have the same physical appearance as the object being modeled is
an analog model
Decision Criteria
are the ways to evaluate the choices faced by the decision maker
Inputs to a quantitative model
are uncertain for a stochastic model.
A negative dual price for a constraint in a minimization problem means
as the right-hand side increases, the objective function value will increase
The volume that results in total revenue being equal to total cost is the
break-even point
The improvement in the value of the objective function per unit increase in a right-hand side is the
dual price
Problem definition
each of the above is true
The field of management science
each of the above is true
Media selection problems usually determine
how many times to use each media source
A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called
infeasible
Slack
is the amount by which the left side of a £ constraint is smaller than the right side
Identification and definition of a problem
is the first step of decision making
A model that uses a system of symbols to represent a problem is called
mathematical
The quantitative analysis approach requires
mathematical expressions for the relationships
A time-series which has a significant upward or downward trend is referred to as
non-stationary
The maximization or minimization of a quantity is the
objective of linear programming
Sensitivity analysis information in computer output is based on the assumption of
one coefficient changes
Management science and operations research both involve
quantitative approaches to decision making
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the
range of optimality
A constraint that does not affect the feasible region is a
redundant constraint
Decision Alternatives
should be identified before decision criteria are established
Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in
standard form
A time-series which has no significant upward or downward trend is referred to as
stationary
When the value of the output cannot be determined even if the value of the controllable input is known, the model is
stochastic
Decision variables
tell how much or how many of something to produce, invest, purchase, hire, etc.
If a decision variable is not positive in the optimal solution, its reduced cost is
the amount its objective function value would need to improve before it could become positive
The dual price measures, per unit increase in the right hand side of the constraint
the change in the value of the optimal solution
In a multicriteria decision problem
the decision maker must evaluate each alternative with respect to each criterion
A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD ³ 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?
the dual price for the HD constraint is -10
The first step in problem solving is
the identification of a difference between the actual and desired state of affairs
An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is
the maximum premium (say for overtime) over the normal price that the company would be willing to pay
The range of feasibility measures
the right-hand-side values for which the dual prices will not change
George Dantzig is important in the history of management science because he developed
the simplex method for linear programming
As long as the slope of the objective function stays between the slopes of the binding constraints
the values of the dual variables won't change
A constraint with a positive slack value
will have a dual price of zero
