Question 1

Minimizing the amount of scrap material generated by cutting steel,leather or fabric from a roll or sheet of stock material is one kind of problem that cannot be solved by linear programming.

Accepted Answer

This statement is false. The problem of minimizing scrap material generated by cutting can be formulated as a linear programming problem, by defining decision variables for the cuts and using constraints that represent the size and shape of the stock material and the desired pieces. There are various techniques and algorithms that can be used to solve such linear programming problems, including the simplex method and interior point methods.

Question 2

Linear programming is useless when resources are plentiful relative to demand.

Accepted Answer

Linear programming is designed to optimize limited resources to meet the demands of a problem. When resources are plentiful relative to demand, there is no need to optimize their allocation using linear programming techniques.

Question 3

Which of the following is an essential condition in a situation for linear programming to be useful?

Accepted Answer

Homogeneity is an essential condition for linear programming to be useful. This means that the relationships between the variables and constraints are linear, and the objective function can be expressed as a linear combination of the variables. Nonlinear constraints, bottlenecks in the objective function, competing objectives, and uncertainty do not necessarily make linear programming useless, but they can make it more difficult to solve or require different methods.

Question 4

In the formulation of a linear programming model we expect to see a requirement on all the decision variables to be either zero or some positive value.

Accepted Answer

This is because in linear programming, the decision variables represent quantities that we are trying to optimize. The requirement for them to be zero or positive ensures that we are only considering feasible solutions in the problem space. Negative decision variables do not make practical sense and would not contribute to a valid solution.

Question 5

Finding the optimal way to use aircraft and their operating crews to provide transportation services to customers to be moved between different locations is one kind of problem that can be solved by linear programming.

Accepted Answer

Linear programming is a mathematical method for optimizing a linear objective function subject to linear constraints. It can be used to solve transportation problems, production planning, financial planning, and many other real-world problems, including the optimal use of aircraft and crews for transportation services.

Question 6

Finding the optimal routing for a product that must be processed sequentially through several machine centers,with each machine in a center having its own cost and output characteristics cannot be solved using linear programming.

Accepted Answer

Linear programming can be used to solve such problems by formulating them as optimization problems with constraints representing the sequence and capacities of the machine centers.

Question 7

Linear programming is gaining wide acceptance in many industries due to the availability of detailed operating information and the interest in optimizing processes to reduce cost.

Accepted Answer

Linear programming is a widely used tool in industries for optimizing operations and reducing costs by analyzing and utilizing detailed operating information.

Question 8

A common application of linear programming is in materials handling.

Accepted Answer

Linear programming can be used in materials handling to optimize resource allocation, such as the allocation of transportation resources for moving materials or the allocation of warehouse space for storing materials.

Question 9

Finding the optimal product mix where several products have different costs and resource requirements cannot be solved using linear programming.

Accepted Answer

Linear programming is a mathematical method used to determine the best possible outcome in a given mathematical model, and it can be used to solve problems involving the optimal product mix with different costs and resource requirements.

Question 10

If products and resources can not be subdivided into fractions,the condition of divisibility is violated.In these cases,a modification of linear programming called integral programming can be used.

Accepted Answer

The answer of If products and resources can not be...

Question 11

Excel Solver solutions include a sensitivity report.This report gives information on making changes in objective function coefficients.

Accepted Answer

The sensitivity report in Excel Solver provides information on how changes in objective function coefficients (and other inputs) affect the optimal solution. Therefore, A is the correct answer.

Question 12

Finding the optimal combination of products to stock in a retail store cannot be solved using linear programming.

Accepted Answer

Linear programming can be used to optimize the allocation of resources among different products, including deciding how much of each product to stock in a retail store based on factors such as demand, pricing, and storage costs. Therefore, finding the optimal combination of products to stock in a retail store can be solved using linear programming.

Question 13

If products and resources can not be subdivided into fractions,the condition of divisibility is violated.In these cases,a modification of linear programming called integer programming can be used.

Accepted Answer

Integer programming is used when the decision variables have to take integer values, usually due to practical considerations such as indivisibility of resources or the need for whole units in the solution. When the condition of divisibility is violated, integer programming is used.

Question 14

Finding the optimal location of a new plant by evaluating shipping costs between alternative locations and supply and demand sources is one kind of problem that can be solved by linear programming.

Accepted Answer

Linear programming is a mathematical technique that can be used to optimize a linear objective function subject to constraints. In the case of finding the optimal location of a new plant, the objective function could be minimizing shipping costs, and the constraints could include supply and demand sources, transportation capacities, and other relevant factors. Therefore, linear programming can be a useful tool in solving this kind of problem.

Question 15

The objective function in a linear programming model can be nonlinear.

Accepted Answer

In linear programming, the objective function must be a linear equation, meaning it is composed of linear terms without any exponents or nonlinear components.

Question 16

Each term in a linear program's objective function should be expressed in the same units.

Accepted Answer

This is true because all terms in the objective function must be added or subtracted together in order to calculate the overall value of the objective function. If the terms are expressed in different units, this would not be mathematically meaningful.

Question 17

Linear programming is a single-objective model,meaning that it has a single objective function to be maximized or minimized.

Accepted Answer

Linear programming has a single objective function to be maximized or minimized.

Question 18

The decision variables in a linear programming model must be non-negative.

Accepted Answer

The decision variables in a linear programming model represent quantities or amounts that can be increased or decreased, but they cannot have negative values in most practical situations. This is because negative values represent "anti-resources" or negative quantities that do not make physical or economic sense. Therefore, in order to ensure that the model makes sense and reflects the reality of the problem, the decision variables are typically constrained to be non-negative. This means that they can be zero or positive, but not negative.

Question 19

Linear programming is useful when resources are unlimited.

Accepted Answer

Linear programming is actually useful when resources are limited, and one needs to allocate them in the best possible way to achieve a desired outcome.

Question 20

In the conventional formulation of a linear programming model we will see all of the decision variables on the right-hand-side of a constraint and a constant value on the left-hand-side.

Accepted Answer

In the conventional formulation of a linear programming model, the decision variables are typically on the left-hand-side of a constraint and a constant value is on the right-hand-side. This convention allows for easy interpretation of the constraints as limiting factors on the decision variables.

Quiz 21: Linear Programming Using the Excel Solver