Question 1

A feasible solution violates at least one of the constraints.

Accepted Answer

A feasible solution satisfies all the constraints. If a solution violates any of the constraints, it is infeasible.

Question 2

In linear programming models , objective functions can only be maximized.

Accepted Answer

In linear programming models, objective functions can be either maximized or minimized depending on the problem being solved.

Question 3

When using the graphical method, only one of the four quadrants of an xy-axis needs to be drawn.

Accepted Answer

True, because only the quadrant(s) that contains the solutions need to be drawn.

Question 4

The equation 8xy = 32 satisfies the proportionality property of linear programming.

Accepted Answer

The equation 8xy = 32 does not represent a linear function because it involves the product of the variables x and y, making it a nonlinear equation. Linear programming involves linear equations or inequalities.

Question 5

Proportionality means the slope of a constraint is proportional to the slope of the objective function.

Accepted Answer

Proportionality means that there is a constant ratio between the slope of a constraint and the slope of the objective function.

Question 6

Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints.

Accepted Answer

Linear programming is indeed a model that represents a firm's decisions using linear relationships, subject to constraints on resources, with an objective to maximize or minimize a function.

Question 7

A constraint is a linear relationship representing a restriction on decision making.

Accepted Answer

A constraint is a linear relationship that represents a restriction on decision making. It can limit the values that decision variables can take on and is often used in optimization problems to ensure that solutions meet certain requirements or objectives.

Question 8

Typically, finding a corner point for the feasible region involves solving a set of three simultaneous equations.

Accepted Answer

Finding a corner point for the feasible region involves finding the intersection of two or more boundary constraints, which can be done graphically or through linear programming techniques such as simplex method. It does not necessarily involve solving a set of three simultaneous equations.

Question 9

The terms in the objective function or constraints are multiplicative.

Accepted Answer

In linear programming, the terms in the objective function and constraints are additive, not multiplicative.

Question 10

All model parameters are assumed to be known with certainty.

Accepted Answer

Model parameters are assumed to be known with certainty, so there is no uncertainty in the model.

Question 11

The feasible solution area contains infinite solutions to the linear program.

Accepted Answer

The feasible solution area of a linear program usually contains infinite solutions, unless it is a degenerate case where there is a unique solution. This is because a linear program typically has multiple ways of obtaining optimal solutions that satisfy the constraints.

Question 12

A linear programming model consists of only decision variables and constraints.

Accepted Answer

A linear programming model consists of decision variables, constraints, and an objective function.

Question 13

The values of decision variables are continuous or divisible.

Accepted Answer

Decision variables in a continuous optimization problem can take on any value within a certain range, including non-integer values. Therefore, they are divisible and not restricted to integer values.

Question 14

A parameter is a numerical value in the objective function and constraints.

Accepted Answer

A parameter is a numerical value that appears in the objective function and constraints of a mathematical model. It is often used to represent some fixed value or condition, such as the cost of a product or the maximum capacity of a machine.

Question 15

Linear programming models exhibit linearity among all constraint relationships and the objective function.

Accepted Answer

Linear programming models are characterized by linearity in all their constraint relationships and the objective function. This means that the mathematical expressions representing the constraints and the objective function involve only first-degree (linear) terms in the decision variables.

Question 16

All linear programming models exhibit a set of constraints.

Accepted Answer

Linear programming models involve maximizing or minimizing an objective function subject to a set of constraints, which are usually expressed as linear inequalities or equations. Therefore, all linear programming models exhibit a set of constraints.

Question 17

The objective function always consists of either maximizing or minimizing some value.

Accepted Answer

The objective function is a mathematical function that is either maximized or minimized depending on the application.

Question 18

The terms in the objective function or constraints are additive.

Accepted Answer

The terms in the objective function or constraints are indeed additive, meaning that the values of the variables can be added together to compute the total value of the function or constraint. This is a fundamental property of linear programming.

Question 19

The objective function is a linear relationship reflecting the objective of an operation.

Accepted Answer

The objective function is a mathematical representation of the objective of an operation which is usually in the form of a linear relationship between the decision variables and the objective.

Question 20

Objective functions in linear programs always minimize costs.

Accepted Answer

Objective functions in linear programs can minimize or maximize any variable, not just costs. It depends on the problem being analyzed.

Quiz 2: Linear Programming: Model Formulation and Graphical Solution