Question 1

In which part(s)of a linear programming formulation would the decision variables be stated?
A)objective function and the left-hand side of each constraint
B)objective function and the right-hand side of each constraint
C)the left-hand side of each constraint only
D)the objective function only

Accepted Answer

The decision variables represent the quantities to be determined or optimized in a linear programming problem. These variables are typically included in the objective function and on the left-hand side of each constraint. Therefore, option A is the correct choice.

Question 2

When no solution to the linear programming problem satisfies all the constraints,including the nonnegativity conditions,it is considered
A)optimal.
B)feasible.
C)infeasible.
D)semifeasible.

Accepted Answer

When no solution satisfies all the constraints including the nonnegativity conditions, it means that the problem is infeasible. Infeasibility occurs when the constraints are contradictory or inconsistent, or when the feasible region is empty. Therefore, option C is the correct answer. Option A, optimal, refers to a feasible solution that optimizes the objective function. Option B, feasible, is a solution that satisfies all the constraints, including the nonnegativity conditions. Option D, semifeasible, is not a valid term in linear programming.

Question 3

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁)or 125 wiffle balls (x₂)can be produced per hour of labor,which of the following constraints reflects this situation? A)300x₁ + 125x₂ > 4,000 B)300x₁ + 125x₂ < 4,000 C)425(x₁ + x₂)< 4,000 D)300x₁ + 125x₂ = 4,000

Accepted Answer

The constraint should represent the maximum amount of hours of labor available to produce the ping-pong balls (300x₁) and the wiffle balls (125x₂). Since this amount cannot exceed the total amount of labor available (4,000), the correct constraint is 300x₁ + 125x₂ < 4,000. Therefore, the answer is choice B.

Question 4

Which of the following special cases does NOT require reformulation of the problem in order to obtain a solution?
A)alternative optimality
B)infeasibility
C)unboundedness
D)Each case requires a reformulation.

Accepted Answer

Alternative optimality does not inherently require a reformulation of the problem to obtain a solution, as it indicates the existence of multiple optimal solutions within the feasible region of the problem.

Question 5

Solve the following system of simultaneous equations.6X + 2Y = 50
2X + 4Y = 20

Accepted Answer

The answer of Solve the following system of simultaneous equations.6X...

Question 6

The amount by which the left side of a less-than-or-equal-to constraint is smaller than the right side
A)is known as a surplus.
B)is known as slack.
C)is optimized for the linear programming problem.
D)exists for each variable in a linear programming problem.

Accepted Answer

The amount by which the left side of a less-than-or-equal-to constraint is smaller than the right side is known as slack. Surplus is the amount by which the left side exceeds the right side in a greater-than-or-equal-to constraint. Option C is incorrect as optimization is done for the objective function and not for constraints. Option D is also incorrect as slack or surplus exists only for constraints and not for variables.

Question 7

Consider the following linear programming problem:  ​ 
a.Use a graph to show each constraint and the feasible region.
b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution?
c.What is the optimal value of the objective function?

Accepted Answer

The answer of Consider the following linear programming problem: ...

Question 8

A redundant constraint results in
A)no change in the optimal solution(s).
B)an unbounded solution.
C)no feasible solution.
D)alternative optimal solutions.

Accepted Answer

Redundant constraints do not affect the feasible region or alter the optimal solution, hence there is no change in the optimal solution(s).

Question 9

All of the following statements about a redundant constraint are correct EXCEPT
A)a redundant constraint does not affect the optimal solution.
B)a redundant constraint does not affect the feasible region.
C)recognizing a redundant constraint is easy with the graphical solution method.
D)at the optimal solution,a redundant constraint will have zero slack.

Accepted Answer

A redundant constraint does not necessarily have zero slack at the optimal solution; it may have positive slack, indicating that it does not bind or affect the solution.

Question 10

Solve the following system of simultaneous equations.6X + 4Y = 40
2X + 3Y = 20

Accepted Answer

The answer of Solve the following system of simultaneous equations.6X...

Question 11

The three assumptions necessary for a linear programming model to be appropriate include all of the following EXCEPT
A)proportionality.
B)additivity.
C)divisibility.
D)normality.

Accepted Answer

The assumption of normality is not necessary for a linear programming model. The other three assumptions (proportionality, additivity, and divisibility) are essential for the model to be appropriate.

Question 12

Which of the following is a valid objective function for a linear programming problem? A)Min 8xy B)Min 4x + 3y + (1/2)z C)Min 5x² + 6y² D)Max (x₁ + x₂)/x₃

Accepted Answer

A valid objective function for linear programming must be a linear function of the decision variables. Option B is the only linear function among the given options. Option A has a product of decision variables, while option C has decision variables raised to a power. Option D includes a ratio of decision variables, which is not a linear function. Therefore, the best choice is B.

Question 13

For the following linear programming problem,determine the optimal solution using the graphical solution method.

Accepted Answer

The answer of For the following linear programming problem,determine the...

Question 14

To find the optimal solution to a linear programming problem using the graphical method,
A)find the feasible point that is the farthest away from the origin.
B)find the feasible point that is at the highest location.
C)find the feasible point that is closest to the origin.
D)None of these are correct.

Accepted Answer

The optimal solution to a linear programming problem using the graphical method is found by identifying the feasible region and then applying the objective function to find the point(s) that maximize or minimize the objective. This does not necessarily involve finding points closest to or farthest from the origin, or at the highest location. The correct approach depends on the direction of the objective function and the shape of the feasible region.

Question 15

A constraint that does NOT affect the feasible region of the solution is a
A)nonnegativity constraint.
B)redundant constraint.
C)standard constraint.
D)slack constraint.

Accepted Answer

A redundant constraint is one that is already implied by the other constraints in the problem, so adding it does not affect the feasible region. Nonnegativity constraints are important constraints that do affect the feasible region. Standard and slack constraints are not types of constraints.

Question 16

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a
A)standard variable.
B)slack variable.
C)surplus variable.
D)nonnegative variable.

Accepted Answer

A slack variable is added to the left-hand side of a less-than-or-equal-to constraint in linear programming to convert the inequality into an equality, allowing the problem to be solved using methods that require equations, such as the Simplex algorithm.

Question 17

Decision variables
A)are values that are used to determine how much or how many of something to produce,invest,etc.
B)represent the values of the constraints.
C)are values that measure the objective function.
D)must be unique for each constraint.

Accepted Answer

Decision variables are the values that are being decided upon in a decision-making problem. They are the quantities or values that are being produced, invested, purchased, sold, etc. in order to satisfy a particular objective.

Question 18

All linear programming problems have all of the following properties EXCEPT
A)a linear objective function that is to be maximized or minimized.
B)a set of linear constraints.
C)alternative optimal solutions.
D)variables that are all restricted to nonnegative values.

Accepted Answer

Not all linear programming problems have alternative optimal solutions, as some may have only one unique optimal solution.

Question 19

Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in
A)standard form.
B)bounded form.
C)feasible form.
D)alternative form.

Accepted Answer

Standard form is a type of linear programming problem where all the constraints are expressed as equalities and all variables are non-negative. This form allows for the use of efficient algorithms to solve the problem. Bounded form, feasible form, and alternative form are not recognized terms in linear programming.

Question 20

Which of the following statements is NOT true?
A)A feasible solution satisfies all constraints.
B)An optimal solution satisfies all constraints.
C)An infeasible solution violates all constraints.
D)A feasible solution point does not have to lie on the boundary of the feasible region.

Accepted Answer

An infeasible solution does not necessarily violate all constraints; it violates at least one constraint, making it not feasible.

Quiz 2: An Introduction to Linear Programming

In which part(s) of a linear programming formulation would the decision variables be stated?

When no solution to the linear programming problem satisfies all the constraints,including the nonnegativity conditions,it is considered

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁) or 125 wiffle balls (x₂) can be produced per hour of labor,which of the following constraints reflects this situation?

Which of the following special cases does NOT require reformulation of the problem in order to obtain a solution?

Solve the following system of simultaneous equations.6X + 2Y = 50 2X + 4Y = 20

The amount by which the left side of a less-than-or-equal-to constraint is smaller than the right side

Consider the following linear programming problem: a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optimal value of the objective function?

A redundant constraint results in

All of the following statements about a redundant constraint are correct EXCEPT

Solve the following system of simultaneous equations.6X + 4Y = 40 2X + 3Y = 20

The three assumptions necessary for a linear programming model to be appropriate include all of the following EXCEPT

Which of the following is a valid objective function for a linear programming problem?

For the following linear programming problem,determine the optimal solution using the graphical solution method.

To find the optimal solution to a linear programming problem using the graphical method,

A constraint that does NOT affect the feasible region of the solution is a

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a

Decision variables

All linear programming problems have all of the following properties EXCEPT

Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in

Which of the following statements is NOT true?

Quiz 2: An Introduction to Linear Programming

In which part(s) of a linear programming formulation would the decision variables be stated?

When no solution to the linear programming problem satisfies all the constraints,including the nonnegativity conditions,it is considered

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor,which of the following constraints reflects this situation?

Which of the following special cases does NOT require reformulation of the problem in order to obtain a solution?

Solve the following system of simultaneous equations.6X + 2Y = 50 2X + 4Y = 20

The amount by which the left side of a less-than-or-equal-to constraint is smaller than the right side

Consider the following linear programming problem: ​ a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optimal value of the objective function?

A redundant constraint results in

All of the following statements about a redundant constraint are correct EXCEPT

Solve the following system of simultaneous equations.6X + 4Y = 40 2X + 3Y = 20

The three assumptions necessary for a linear programming model to be appropriate include all of the following EXCEPT

Which of the following is a valid objective function for a linear programming problem?

For the following linear programming problem,determine the optimal solution using the graphical solution method.

To find the optimal solution to a linear programming problem using the graphical method,

A constraint that does NOT affect the feasible region of the solution is a

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is a

Decision variables

All linear programming problems have all of the following properties EXCEPT

Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in

Which of the following statements is NOT true?

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁) or 125 wiffle balls (x₂) can be produced per hour of labor,which of the following constraints reflects this situation?

Consider the following linear programming problem: a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optimal value of the objective function?