Question 1

If a problem is infeasible then:
A)it was not formulated correctly.
B)it is the constraints that are to blame,not the objective function.
C)at least one of the decision variable will have an optimal value of infinity.
D)None of the above.
E)All of the above.

Accepted Answer

The answer of If a problem is infeasible then:
A)it was...

Question 2

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:
A)1.
B)2.
C)30.
D)100.
E)unlimited.

Accepted Answer

There is no theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem. However, as the number of variables increases, the computation time required to solve the problem may become prohibitive. In practice, the largest problems that can be solved using the simplex method typically have tens or hundreds of thousands of variables.

Question 3

If a problem is unbounded then:
A)the problem may not have been formulated correctly.
B)the data may not have been entered correctly.
C)at least one of the decision variable will have an optimal value of $\infty$.
D)None of the above.
E)All of the above.

Accepted Answer

The answer of If a problem is unbounded then:
A)the problem...

Question 4

If a problem has more than one optimal solution then:
A)the slope of the objective function line is the same as one of the constraints.
B)the problem was not formulated correctly.
C)the problem must be re-solved.
D)All of the above.
E)None of the above.

Accepted Answer

The answer of If a problem has more than one...

Question 5

The computer time per iteration for an interior-point algorithm is approximately the same as for the simplex method.

Accepted Answer

The interior-point algorithm typically requires more computing time per iteration compared to the simplex method. This is because in each iteration of the interior-point algorithm, a system of equations must be solved to obtain the search direction, which can be computationally expensive.

Question 6

The simplex method is a specific type of interior-point algorithm.

Accepted Answer

The simplex method is a different type of algorithm commonly used for linear programming, but it is not an interior-point algorithm.

Question 7

For any linear programming problem,the best corner point must be an optimal solution.

Accepted Answer

The answer of For any linear programming problem,the best corner...

Question 8

Interior-point algorithms have limited capability for what-if analysis.
Multiple Choice Questions

Accepted Answer

Interior-point algorithms are often used for solving linear and quadratic programming problems efficiently, but they do not perform well for what-if analysis which involves sensitivity analysis and exploring different scenarios. Other techniques such as Monte Carlo simulations or scenario analysis are better suited for what-if analysis.

Question 9

Management may choose a single product mix from among multiple optimal solutions because of:
A)a desire to highlight a new product.
B)needs of an important customer.
C)strategies adopted by competitors.
D)All of the above.
E)None of the above.

Accepted Answer

All of the above are reasons why management may choose a single product mix from among multiple optimal solutions. A company may choose to highlight a new product by including it in the product mix, cater to the needs of an important customer by offering specific products, or adopt strategies to compete with competitors by adjusting their product mix.

Question 10

The simplex method only considers adjacent corner points.

Accepted Answer

The simplex method is a method of solving linear programming problems by considering adjacent corner points (vertices) of the feasible region, and moving from one vertex to another along an edge in order to improve the objective function until an optimal solution is reached. Therefore, it only considers adjacent corner points.

Question 11

If a maximization problem has an objective function of 3x₁ + 10x₂,which of the following corner points is the optimal solution? A)(0,2). B)(0,3). C)(3,3). D)(5,1). E)(0,0).

Accepted Answer

To find the optimal solution, we need to evaluate the objective function at each of the corner points and choose the one that yields the highest value.

- At (0,0): 3(0)(1)(1)(0) + 10(0)(2)(1)(0) = 0
- At (0,2): 3(0)(1)(1)(2) + 10(0)(2)(1)(2) = 0
- At (0,3): 3(0)(1)(2)(3) + 10(0)(2)(1)(3) = 0
- At (3,3): 3(3)(1)(2)(3) + 10(3)(2)(1)(3) = 117

Therefore, the optimal solution is at (3,3) and the answer is choice C.

Question 12

The simplex method chooses the adjacent corner point that is closest when searching for an optimal solution.

Accepted Answer

The simplex method does not necessarily choose the adjacent corner point that is closest, but rather follows a systematic process of moving along the edges of the feasible region until an optimal solution is found.

Question 13

Two corner points are adjacent to each other if they share all but one of the same constraint boundaries.

Accepted Answer

This is the correct definition of adjacent corner points in linear programming.

Question 14

Whenever possible,the initialization step of the simplex method chooses the origin to be the initial corner point.

Accepted Answer

It is true that whenever possible, the simplex method chooses the origin as the initial corner point because it is often the easiest point to start from and reduces the number of iterations needed to reach the optimal solution. However, there may be cases where the origin cannot be used as the initial point, such as when there are constraints that prevent it from being a feasible solution.

Question 15

If a problem is infeasible,the Solver will show the message "Set Cell values do not converge".

Accepted Answer

If a problem is infeasible, the Solver will show the message "Solver could not find a feasible solution."

Question 16

A linear programming problem may have: I.no optimal solutions.
II)exactly one optimal solution.
III)as many optimal solutions as there are decision variables.
IV)an infinite number of optimal solutions.
A)II and IV only.
B)II and III only.
C)I,II,and III only.
D)I,II,and IV only.
E)All of the above.

Accepted Answer

A linear programming problem can have no optimal solutions if it is infeasible or unbounded, exactly one optimal solution if the optimal point is unique, or an infinite number of optimal solutions if the objective function is parallel to a constraint over a feasible region.

Question 17

Management science algorithms are typically iterative algorithms.

Accepted Answer

Management science algorithms typically involve repetitive calculations and adjustments until an optimal solution is reached, making them iterative algorithms.

Question 18

In a linear programming problem,when the objective function is parallel to one of the constraints,then:
A)the solution is not optimal.
B)multiple optimal solutions may exist.
C)a single corner point optimal solution exists.
D)no feasible solution exists.
E)None of the above.

Accepted Answer

When the objective function is parallel to one of the constraints, the constraint becomes non-binding, meaning it does not affect the optimal solution. This results in the possibility of multiple optimal solutions where the objective function is parallel to those constraints.

Question 19

The simplex method is the standard procedure for solving linear programming problems with any number of decision problems because:
A)it is an efficient procedure.
B)spreadsheets are not always available.
C)it provides the information necessary for what-if analysis.
D)a and b only.
E)a and c only.

Accepted Answer

The simplex method is an efficient procedure for solving linear programming problems and also provides the necessary information for what-if analysis. Therefore, choices A and C are correct. The availability of spreadsheets does not affect the suitability of the simplex method, so choice B is incorrect.

Question 20

If a maximization problem has an objective function of 3x₁ + 2x₂,which of the following corner points is the optimal solution? A)(0,2). B)(0,3). C)(3,3). D)(5,1). E)(0,0).

Accepted Answer

To determine the optimal solution, we need to evaluate the objective function at each corner point and choose the one that gives the highest value. Corner point (0,2): 3x₁ + 2x₂ = 3(0)(1)(1)(2) + 2(0)(1)(2)(2) = 0 Corner point (0,3): 3x₁ + 2x₂ = 3(0)(1)(1)(3) + 2(0)(1)(2)(3) = 0 Corner point (3,3): 3x₁ + 2x₂ = 3(3)(1)(1)(3) + 2(3)(1)(2)(3) = 33 Corner point (5,1): 3x₁ + 2x₂ = 3(5)(1)(1)(1) + 2(5)(1)(2)(1) = 25 Corner point (0,0): 3x₁ + 2x₂ = 3(0)(1)(1)(0) + 2(0)(1)(2)(0) = 0 The highest value is obtained at corner point (5,1), with an objective function value of 25. Therefore, the optimal solution is (5,1).

Quiz 17: CD - Solution Concepts for Linear Programming

If a problem is infeasible then:

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

If a problem is unbounded then:

If a problem has more than one optimal solution then:

The computer time per iteration for an interior-point algorithm is approximately the same as for the simplex method.

The simplex method is a specific type of interior-point algorithm.

For any linear programming problem,the best corner point must be an optimal solution.

Interior-point algorithms have limited capability for what-if analysis. Multiple Choice Questions

Management may choose a single product mix from among multiple optimal solutions because of:

The simplex method only considers adjacent corner points.

If a maximization problem has an objective function of 3x₁ + 10x₂,which of the following corner points is the optimal solution?

The simplex method chooses the adjacent corner point that is closest when searching for an optimal solution.

Two corner points are adjacent to each other if they share all but one of the same constraint boundaries.

Whenever possible,the initialization step of the simplex method chooses the origin to be the initial corner point.

If a problem is infeasible,the Solver will show the message "Set Cell values do not converge".

A linear programming problem may have: I.no optimal solutions. II) exactly one optimal solution. III) as many optimal solutions as there are decision variables. IV) an infinite number of optimal solutions.

Management science algorithms are typically iterative algorithms.

In a linear programming problem,when the objective function is parallel to one of the constraints,then:

The simplex method is the standard procedure for solving linear programming problems with any number of decision problems because:

If a maximization problem has an objective function of 3x₁ + 2x₂,which of the following corner points is the optimal solution?

Quiz 17: CD - Solution Concepts for Linear Programming

If a problem is infeasible then:

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

If a problem is unbounded then:

If a problem has more than one optimal solution then:

The computer time per iteration for an interior-point algorithm is approximately the same as for the simplex method.

The simplex method is a specific type of interior-point algorithm.

For any linear programming problem,the best corner point must be an optimal solution.

Interior-point algorithms have limited capability for what-if analysis. Multiple Choice Questions

Management may choose a single product mix from among multiple optimal solutions because of:

The simplex method only considers adjacent corner points.

If a maximization problem has an objective function of 3x1 + 10x2,which of the following corner points is the optimal solution?

The simplex method chooses the adjacent corner point that is closest when searching for an optimal solution.

Two corner points are adjacent to each other if they share all but one of the same constraint boundaries.

Whenever possible,the initialization step of the simplex method chooses the origin to be the initial corner point.

If a problem is infeasible,the Solver will show the message "Set Cell values do not converge".

A linear programming problem may have: I.no optimal solutions. II) exactly one optimal solution. III) as many optimal solutions as there are decision variables. IV) an infinite number of optimal solutions.

Management science algorithms are typically iterative algorithms.

In a linear programming problem,when the objective function is parallel to one of the constraints,then:

The simplex method is the standard procedure for solving linear programming problems with any number of decision problems because:

If a maximization problem has an objective function of 3x1 + 2x2,which of the following corner points is the optimal solution?

If a maximization problem has an objective function of 3x₁ + 10x₂,which of the following corner points is the optimal solution?

If a maximization problem has an objective function of 3x₁ + 2x₂,which of the following corner points is the optimal solution?