Question 1

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

Accepted Answer

Profit maximization is the objective function in an LP problem, not a decision variable. Decision variables are the unknown quantities that need to be determined in order to optimize the objective function, such as the quantity of a certain product to produce or the amount of a particular resource to allocate.

Question 2

Every constraint in a maximization problem has a slack variable.

Accepted Answer

Not every constraint in a maximization problem has a slack variable; only less-than-or-equal-to constraints use slack variables to convert them into equalities.

Question 3

A linear programming problem can have multiple optimal solutions.

Accepted Answer

A linear programming problem can have multiple extreme points that all yield the same optimal objective function value, leading to multiple optimal solutions.

Question 4

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

Accepted Answer

The value of an objective function can increase, decrease, or remain constant as it is moved away from the origin, depending on the specific function and the direction of movement.

Question 5

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

Accepted Answer

The term "isoprofit" is derived from the Greek prefix "iso" meaning equal, and "profit" meaning the financial gain obtained from a business activity. Therefore, an isoprofit line denotes a line on a graph connecting all points that yield the same level of profit.

Question 6

Linear programming techniques will produce an optimal solution to problems that involve limitations on resources.

Accepted Answer

Linear programming techniques are designed to find the best solution within a set of constraints or limitations. Therefore, it will produce an optimal solution that meets these limitations or constraints.

Question 7

The graphical Solution Method can handle problems that involve any number of decision variables.

Accepted Answer

The graphical solution method is typically limited to problems with two decision variables because it relies on plotting solutions on a two-dimensional graph. For problems with more than two decision variables, other methods such as the simplex method are used.

Question 8

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

Accepted Answer

The equation is linear because each term is either a constant or a multiple of one variable, and the degree of each term is 1.

Question 9

For a nonbinding constraint,if the left side is greater than the right side,we say that there is surplus; if the left side is smaller than the right side,we say that there is slack.

Accepted Answer

This statement correctly describes the meaning of surplus and slack in the context of nonbinding constraints.

Question 10

LP problems must have a single goal or objective specified.

Accepted Answer

LP problems must have a single goal or objective specified, which is usually to maximize or minimize a linear function of the decision variables.

Question 11

Constraints limit the alternatives available to a decision-maker.

Accepted Answer

Constraints restrict the options or alternatives available to a decision-maker, making them choose only from a limited set of possibilities.

Question 12

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 13

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" or the "Extreme Point Theorem". It states that if a linear programming problem has a finite optimal solution, then that solution will occur at one of the corner points of the feasible region (also known as vertices or extreme points).

Question 14

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 15

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 because it alters the relative values of the decision variables in the objective function, potentially leading to a different set of values for these variables that maximizes or minimizes the objective.

Question 16

The simplex method is an LP algorithm that can solve problems having more than two decision variables.

Accepted Answer

The simplex method is a widely used LP algorithm that can solve problems with any number of decision variables.

Question 17

The removal of a redundant constraint does not affect the feasible solution space.

Accepted Answer

A redundant constraint is one that can be derived from other constraints already in the system. Therefore, removing it does not change the feasible solution space because it does not actually eliminate any valid solutions.

Question 18

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

Accepted Answer

The feasible solution space is the set of all points that satisfy all constraints. Therefore, any point in the feasible solution space satisfies all constraints.

Question 19

The equation 3xy = 9 is linear.

Accepted Answer

The answer of The equation 3xy = 9 is linear....

Question 20

An objective function represents a family of parallel lines.

Accepted Answer

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

Quiz 9: Linear Programming