Deck 12: Linear Optimization Models

Question 1

The points where constraints intersect on the boundary of the feasible region are termed as the

A)feasible points.
B)objective function contour.
C)extreme points.
D)feasible edges.

Answer 1

extreme points.

Question 2

A __________ refers to a constraint that can be expressed as an equality at the optimal solution.

A)nonnegativity constraint
B)first class constraint
C)slack variable
D)binding constraint

Answer 2

binding constraint

Question 3

A variable subtracted from the left-hand side of a greater-than-or-equal to constraint to convert the constraint into an equality is known as a(n)

A)surplus variable.
B)slack variable.
C)unbounded variable.
D)binding constraint.

Answer 3

surplus variable.

Question 4

When formulating a constraint, care must be taken to ensure that

A)all the objective function coefficients are included.
B)there are no inequalities in the mathematical expression.
C)the decision variables are set at either maximum or minimum values.
D)the units of measurement on both sides of the constraint match.

Question 5

Geometrically, binding constraints intersect to form the

A)subspace.
B)optimal point.
C)decision cell.
D)zero slack.

Question 6

Constraints are

A)quantities to be maximized in a linear programming model.
B)quantities to be minimized in a linear programming model.
C)restrictions that limit the settings of the decision variables.
D)input variables that can be controlled during optimization.

Question 7

In a linear programming model, the __________ assumption plus the nonnegativity constraints mean that decision variables can take on any value greater than or equal to zero.

A)proportionality
B)divisibility
C)additivity
D)negativity

Question 8

The slack value for binding constraints is

A)always a positive integer.
B)zero.
C)a negative integer.
D)equal to the sum of the optimal points in the solution.

Question 9

Which algorithm, developed by George Dantzig and utilized by Excel Solver, is effective at investigating extreme points in an intelligent way to find the optimal solution to even very large linear programs?

A)Ellipsoidal algorithm
B)Complex algorithm
C)Trial-and-error algorithm
D)Simplex algorithm

Question 10

Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit? ​

A)S = 0, D = 0
B)S = 405, D = 0
C)S = 0, D = 299
D)S = 182, D = 145

Question 11

A mathematical function in which each variable appears in a separate term and is raised to the first power is known as a

A)power function.
B)linear function.
C)what-if function.
D)nonlinear function.

Question 12

In problem formulation, the

A)objective is expressed in terms of the decision variables.
B)constraints are expressed in terms of the obtained objective function coefficients.
C)nonnegativity constraints are always ignored.
D)optimal solution is decided upon.

Question 13

A(n) ___________ solution satisfies all the constraint expressions simultaneously.

A)feasible
B)objective
C)infeasible
D)extreme

Question 14

The __________ value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint.

A)objective function coefficient
B)slack
C)unbounded
D)surplus

Question 15

The __________ assumption necessary for a linear programming model to be appropriate means that the contribution to the objective function and the amount of resources used in each constraint are in accordance to the value of each decision variable.

A)proportionality
B)divisibility
C)additivity
D)negativity

Question 16

The assumption that is necessary for a linear programming model to be appropriate and that ensures that the value of the objective function and the total resources used can be found by summing the objective function contribution and the resources used for all decision variables is known as

A)proportionality.
B)negativity.
C)additivity.
D)divisibility.

Question 17

A(n) __________ refers to a set of points that yield a fixed value of the objective function.

A)objective function coefficient
B)infeasible solution
C)objective function contour
D)feasible region

Question 18

__________, or modeling, is the process of translating a verbal statement of a problem into a mathematical statement.

A)Problem-solving approach
B)Data preparation
C)Data structuring
D)Problem formulation

Question 19

The term __________ refers to the expression that defines the quantity to be maximized or minimized in a linear programming model.

A)objective function
B)problem formulation
C)decision variable
D)association rule

Question 20

A controllable input for a linear programming model is known as a

A)parameter.
B)decision variable.
C)dummy variable.
D)constraint.

Question 21

Can a linear programming problem have no solution? More than one solution? Explain.

Question 22

The change in the optimal objective function value per unit increase in the right-hand side of a constraint is given by the

A)objective function coefficient.
B)shadow price.
C)restrictive cost.
D)allowable increase.

Question 23

Rob is a financial manager with Sharez, an investment advisory company. He must select specific investments-for example, stocks and bonds-from a variety of investment alternatives. Which of the following statements is most likely to be the objective function in this scenario?

A)Minimization of the number of stocks held
B)Maximization of expected return
C)Minimization of tax dues
D)Maximization of investment risk

Question 24

A canned food manufacturer has its manufacturing plants in three locations across a state. Their product has to be transported to 3 central distribution centers, which in turn disperse the goods to 72 stores across the state. Which of the following is most likely to be the objective function in this scenario?

A)Increasing the number of goods manufactured at the plant
B)Decreasing the cost of their raw material sourcing
C)Minimizing the cost of shipping goods from the plant to the store
D)Minimizing the quantity of goods distributed across the stores

Question 25

The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as

A)infeasibility.
B)unbounded.
C)infiniteness.
D)semi-optimality.

Question 26

Problems with infeasible solutions arise in practice because

A)management doesn't specify enough restrictions.
B)too many restrictions have been placed on the problem.
C)of errors in objective function formulation.
D)there are too few decision variables.

Question 27

The shadow price of nonbinding constraints

A)will always be zero.
B)will always be a positive value.
C)can never be equal to zero.
D)is no longer valid if the right-hand side of the constraint remains the same.

Question 28

In linear programming models of real problems, the occurrence of an unbounded solution means that the

A)resultant values of the decision variables have no bounds.
B)mathematical models sufficiently represent the real-world problems.
C)problem formulation is improper.
D)constraints have been excessively used in modeling.

Question 29

A canned food manufacturer has its manufacturing plants in three locations across a state. Their product has to be transported to 3 central distribution centers, which in turn disperse the goods to 72 stores across the state. Which of the following visualization tools could help understand this problem better?

A)Time-series plot
B)Scatter chart
C)Network graph
D)Contour plot

Question 30

A scenario in which the optimal objective function contour line coincides with one of the binding constraint lines on the boundary of the feasible region leads to __________ solutions.

A)infeasible
B)alternative optimal
C)binding
D)unique optimal

Question 31

The reduced cost for a decision variable that appears in a Sensitivity Report refers to the __________ of the nonnegativity constraint for that variable.

A)range of optimality
B)slack value
C)shadow price
D)range of feasibility

Question 32

Rob is a financial manager with Sharez, an investment advisory company. He must select specific investments-for example, stocks and bonds-from a variety of investment alternatives. Restrictions on the type of permissible investments would be a __________ in this case.

A)feasible solution
B)surplus variable
C)slack variable
D)constraint

Question 33

Zen, Inc. manufactures two types of products, the G.1 and the T.1 models. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work a 7-hour shift. On an average, to produce a G.1 model, Zen, Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T.1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T.1 models as G.1 models. The company operates five days per week and makes a net profit of $130 on the G.1 model, and $150 on the T.1 model. Zen, Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. Solve Using the Excel Solver tool.
​

Question 34

__________ is the situation in which no solution to the linear programming problem satisfies all the constraints.

A)Unboundedness
B)Divisibility
C)Infeasibility
D)Optimality

Question 35

Zen, Inc. manufactures two types of products, the G.1 and the T.1 models. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work a 7-hour shift. On an average, to produce a G.1 model, Zen, Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T.1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T.1 models as G.1 models. The company operates five days per week and makes a net profit of $130 on the G.1 model, and $150 on the T.1 model. Zen, Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. Formulate the problem.
​
Let G = the number of G.1 product produced each week.
Let T = the number of T.1 product produced each week.
​
Maximize 130G + 150T
s.t.
production's labor constraint 3.5G + 4T ≤ 2030
assembly's labor constraint 2G + 1.5T ≤ 875
​

Question 36

The study of how changes in the input parameters of a linear programming problem affect the optimal solution is known as

A)regression analysis.
B)model analysis.
C)optimality analysis.
D)sensitivity analysis.

Question 37

Which of the following error messages is displayed in Excel Solver when attempting to solve an unbounded problem?

A)Solver could not find a feasible solution.
B)Solver cannot improve the current solution. All constraints are satisfied.
C)Solver could not find a bounded solution.
D)Objective Cell values do not converge.

Question 38

The reduced cost for a decision variable that appears in a Sensitivity Report indicates the change in the optimal objective function value that results from changing the right-hand side of the nonnegativity constraint from

A)1 to 0.
B)0 to 1.
C)-1 to 0.
D)0 to -1.