Question 1

Graphical linear programming can handle problems that involve any number of decision variables.

Accepted Answer

Graphical linear programming is limited to problems with two decision variables because it relies on two-dimensional graphing methods. Problems with more than two variables require other methods due to the limitations of visual representation in two dimensions.

Question 2

The equation 5x + 7y = 10 is linear.

Accepted Answer

The equation is in the standard form of a linear equation and has a degree of 1.

Question 3

LP problems must have a single goal or objective specified.

Accepted Answer

LP problems must have a single goal or objective specified, such as maximizing profit or minimizing costs. This single objective is the primary focus of the LP problem and all constraints must be formulated accordingly.

Question 4

An objective function represents a family of parallel lines.

Accepted Answer

The answer of An objective function represents a family of...

Question 5

The term "iso-profit" line means that all points on the line will yield the same profit.

Accepted Answer

The prefix "iso" means "equal," so an iso-profit line represents all the combinations of inputs that yield the same level of profit. Therefore, all points on the line have the same profit.

Question 6

A maximization problem may be characterized by all greater than or equal to constraints.

Accepted Answer

The answer of A maximization problem may be characterized by...

Question 7

A change in the value of an objective function coefficient does not change the optimal solution.

Accepted Answer

A change in the value of an objective function coefficient can change the optimal solution, as it affects the slope of the objective function line (in graphical methods) or the direction of optimization in higher dimensions, potentially leading to a different set of values for the decision variables that maximize or minimize the objective function.

Question 8

Linear programming techniques will always produce an optimal solution to an LP problem.

Accepted Answer

Linear programming techniques aim to find the optimal solution, but they may not always succeed due to various factors such as unboundedness or infeasibility of the problem.

Question 9

The term "range of optimality" refers to a constraint's right-hand side quantity.

Accepted Answer

The answer of The term "range of optimality" refers to...

Question 10

A linear programming problem can have multiple optimal solutions.

Accepted Answer

It is possible for a linear programming problem to have multiple optimal solutions if the objective function is parallel to a constraint boundary and multiple points on that boundary are optimal solutions.

Question 11

The term "range of feasibility" refers to coefficients of the objective function.

Accepted Answer

The term "range of feasibility" refers to the possible values of the decision variables that satisfy all the constraints in a linear programming problem.

Question 12

The value of an objective function decreases as it is moved away from the origin.

Accepted Answer

There is no general rule that the objective function will decrease as it moves away from the origin. It depends on the specific function and its coefficients. There are cases where the objective function may increase or remain constant as it moves away from the origin.

Question 13

A shadow price indicates how much a one-unit decrease/increase in the right-hand side value of a constraint will decrease/increase the optimal value of the objective function.

Accepted Answer

A shadow price measures the marginal value of a constraint in the objective function. It represents the change in the objective function value resulting from a one-unit increase or decrease in the constraint's right-hand side value, assuming no other changes in the model.

Question 14

If a single optimal solution exists to a graphical LP problem, it will exist at a corner point.

Accepted Answer

This is known as the corner point theorem, which states that if an optimal solution exists for a LP problem, it will occur at one of the corner points (extreme points) of the feasible region.

Question 15

The equation 3xy = 9 is linear.

Accepted Answer

3xy = 9 is a quadratic equation, not a linear equation.

Question 16

An example of a decision variable in an LP problem is profit maximization.

Accepted Answer

Profit maximization is an objective function, not a decision variable. Decision variables are the quantities that the decision-maker can control and manipulate in order to achieve the objective function. Examples of decision variables could be the amount of resources allocated to certain activities, the number of units produced, or the amount of ingredients used in a recipe.

Question 17

Constraints limit the alternatives available to a decision-maker, removing constraints adds viable alternative solutions.

Accepted Answer

Constraints by definition limit the alternatives that can be considered, thus removing them will increase the number of viable alternatives.

Question 18

The feasible solution space only contains points that satisfy all constraints.

Accepted Answer

This is true, as any point outside the feasible solution space would violate at least one constraint.

Question 19

The feasible solution space is the set of all feasible combinations of decision variables as defined by only binding constraints.

Accepted Answer

The feasible solution space is defined by all constraints, not just the binding ones. Binding constraints are those that are exactly met at the optimal solution, while non-binding constraints are those that do not directly affect the optimal solution but still define the feasible region.

Question 20

The simplex method is a general-purpose LP algorithm that can be used for solving only problems with more than six variables.

Accepted Answer

The simplex method can be used for solving LP problems with any number of variables, not just problems with more than six variables.

Quiz 19: Linear Programming