MGMT 3100

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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


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