Question 1

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.

Accepted Answer

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

Question 2

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?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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? ​

Accepted Answer

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

Question 5

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)

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

The slack value for binding constraints is

Accepted Answer

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

Question 12

Constraints are

Accepted Answer

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 13

In problem formulation, the

Accepted Answer

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 14

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
​

Accepted Answer

The answer of Zen, Inc. manufactures two types of products,...

Question 15

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.
​

Accepted Answer

The answer of Zen, Inc. manufactures two types of products,...

Question 16

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?

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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.

Exam 12: Linear Optimization Models