# Decision variables

BMDS 3371 Week 5 Midterm Exam 100% Correct Answers

Each question is worth 2.5 points. The midterm covers chapters 2, 3, 4 and 6.

The midterm is due by Wednesday, April 8, 2015, 11:59pm CST. No exceptions!

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The maximization or minimization of a quantity is the

a. goal of management science.

b. decision for decision analysis.

c. constraint of operations research.

d. objective of linear programming.

Decision variables

a. tell how much or how many of something to produce, invest, purchase, hire, etc.

b. represent the values of the constraints.

c. measure the objective function.

d. must exist for each constraint.

Which of the following is a valid objective function for a linear programming problem?

a. Max 5xy

b. Min 4x + 3y + (2/3)z

c. Max 5×2 + 6y2

d. Min (x1 + x2)/x3

Which of the following statements is NOT true?

a. A feasible solution satisfies all constraints.

b. An optimal solution satisfies all constraints.

c. An infeasible solution violates all constraints.

d. A feasible solution point does not have to lie on the boundary of the feasible region.

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

a. optimal.

b. feasible.

c. infeasible.

d. semi-feasible.

Slack

a. is the difference between the left and right sides of a constraint.

b. is the amount by which the left side of a constraint is smaller than the right side.

c. is the amount by which the left side of a constraint is larger than the right side.

d. exists for each variable in a linear programming problem.

To find the optimal solution to a linear programming problem using the graphical method

a. find the feasible point that is the farthest away from the origin.

b. find the feasible point that is at the highest location.

c. find the feasible point that is closest to the origin.

d. None of the alternatives is correct.

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

a. alternate optimality

b. Infeasibility

c. Unboundedness

d. each case requires a reformulation.

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

a. sensitivity value.

b. dual price.

c. constraint coefficient.

d. slack value.

As long as the slope of the objective function stays between the slopes of the binding constraints

a. the value of the objective function won’t change.

b. there will be alternative optimal solutions.

c. the values of the dual variables won’t change.

d. there will be no slack in the solution.

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

a. at least 1.

b. 0.

c. an infinite number.

d. at least 2.

A constraint that does not affect the feasible region is a

a. non-negativity constraint.

b. redundant constraint.

c. standard constraint.

d. slack constraint.

Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in

a. standard form.

b. bounded form.

c. feasible form.

d. alternative form.

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

a. A redundant constraint does not affect the optimal solution.

b. A redundant constraint does not affect the feasible region.

c. Recognizing a redundant constraint is easy with the graphical solution method.

d. At the optimal solution, a redundant constraint will have zero slack.

All linear programming problems have all of the following properties EXCEPT

a. a linear objective function that is to be maximized or minimized.

b. a set of linear constraints.

c. alternative optimal solutions.

d. variables that are all restricted to nonnegative values.

To solve a linear programming problem with thousands of variables and constraints

a. a personal computer can be used.

b. a mainframe computer is required.

c. the problem must be partitioned into subparts.

d. unique software would need to be developed.

A negative dual price for a constraint in a minimization problem means

a. as the right-hand side increases, the objective function value will increase.

b. as the right-hand side decreases, the objective function value will increase.

c. as the right-hand side increases, the objective function value will decrease.

d. as the right-hand side decreases, the objective function value will decrease.

If a decision variable is not positive in the optimal solution, its reduced cost is

a. what its objective function value would need to be before it could become positive.

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

c. zero.

d. its dual price.

A constraint with a positive slack value

a. will have a positive dual price.

b. will have a negative dual price.

c. will have a dual price of zero.

d. has no restrictions for its dual price.

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

a. optimal solution.

b. dual solution.

c. range of optimality.

d. range of feasibility.

The range of feasibility measures

a. the right-hand-side values for which the objective function value will not change.

b. the right-hand-side values for which the values of the decision variables will not change.

c. the right-hand-side values for which the dual prices will not change.

d. each of these choices are true.

The 100% Rule compares

a. proposed changes to allowed changes.

b. new values to original values.

c. objective function changes to right-hand side changes.

d. dual prices to reduced costs.

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

a. the maximum premium (say for overtime) over the normal price that the company would be willing to pay.

b. the upper limit on the total hourly wage the company would pay.

c. the reduction in hours that could be sustained before the solution would change.

d. the number of hours by which the right-hand side can change before there is a change in the solution point.

A section of output from The Management Scientist is shown here.

Variable Lower Limit Current Value Upper Limit

1 60 100 120

What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

a. Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same.

b. The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.

c. The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.

d. The problem will need to be resolved to find the new optimal solution and dual price.

A section of output from The Management Scientist is shown here.

Constraint Lower Limit Current Value Upper Limit

2 240 300 420

What will happen if the right-hand-side for constraint 2 increases by 200?

a. Nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same.

b. The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.

c. The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.

d. The problem will need to be resolved to find the new optimal solution and dual price.

The dual value on the nonnegativitiy constraint for a variable is that variable’s

a. sunk cost.

b. surplus value.

c. reduced cost.

d. relevant cost.

The dual price measures, per unit increase in the right hand side of the constraint,

a. the increase in the value of the optimal solution.

b. the decrease in the value of the optimal solution.

c. the improvement in the value of the optimal solution.

d. the change in the value of the optimal solution.

Sensitivity analysis information in computer output is based on the assumption of

a. no coefficient changes.

b. one coefficient changes.

c. two coefficients change.

d. all coefficients change.

When the cost of a resource is sunk, then the dual price can be interpreted as the

a. minimum amount the firm should be willing to pay for one additional unit of the resource.

b. maximum amount the firm should be willing to pay for one additional unit of the resource.

c. minimum amount the firm should be willing to pay for multiple additional units of the resource.

d. maximum amount the firm should be willing to pay for multiple additional units of the resource.

Which of the following is not a question answered by sensitivity analysis?

a. If the right-hand side value of a constraint changes, will the objective function value change?

b. Over what range can a constraint’s right-hand side value without the constraint’s dual price possibly changing?

c. By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?

d. By how much will the objective function value change if a decision variable’s coefficient in the objective function changes within the range of optimality?

Media selection problems usually determine

a. how many times to use each media source.

b. the coverage provided by each media source.

c. the cost of each advertising exposure.

d. the relative value of each medium.

To study consumer characteristics, attitudes, and preferences, a company would engage in

a. client satisfaction processing.

b. marketing research.

c. capital budgeting.

d. production planning.

The dual price for a constraint that compares funds used with funds available is .058. This means that

a. the cost of additional funds is 5.8%.

b. if more funds can be obtained at a rate of 5.5%, some should be.

c. no more funds are needed.

d. the objective was to minimize.

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

a. Max 2M + 3B

b. Min 4000 (M + B)

c. Max 8000M + 12000B

d. Min 2M + 3B

Modern revenue management systems maximize revenue potential for an organization by helping to manage

a. pricing strategies.

b. reservation policies.

c. short-term supply decisions.

d. All of the alternatives are correct.

The problem which deals with the distribution of goods from several sources to several destinations is the

a. maximal flow problem

b. transportation problem

c. assignment problem

d. shortest-route problem

The parts of a network that represent the origins are

a. the capacities

b. the flows

c. the nodes

d. the arcs

The objective of the transportation problem is to

a. identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost.

b. minimize the number of origins used to satisfy total demand at the destinations.

c. minimize the number of shipments necessary to satisfy total demand at the destinations.

d. minimize the cost of shipping products from several origins to several destinations.

The number of units shipped from origin i to destination j is represented by

a. xij.

b. xji.

c. cij.

d. cji.

Which of the following is not true regarding the linear programming formulation of a transportation problem?

a. Costs appear only in the objective function.

b. The number of variables is (number of origins) x (number of destinations).

c. The number of constraints is (number of origins) x (number of destinations).

d. The constraints’ left-hand side coefficients are either 0 or 1.