Question 1

The optimal solution to any linear programming model is:
A)the maximum objective function line
B)the minimum objective function line
C)the corner point of a polygon
D)the maximum or minimum of a parabola

Accepted Answer

The optimal solution to a linear programming model occurs at one of the corner points of the feasible region (polygon) since the objective function is linear and can only change its value when one of the constraints becomes binding. Therefore, the solution must occur at a point where at least one constraint is binding, which is only possible at a corner point of the feasible region.

Question 2

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is:
A) 
B) 
C) 
D)

Accepted Answer

C

Question 3

Suppose a company sells two different products,x and y,for net profits of $5 per unit and $10 per unit,respectively.The slope of the line representing the objective function is:
A)0.5
B)-0.5
C)2
D)-2

Accepted Answer

The slope of the objective function represents the rate at which the profit increases with each additional unit sold. Since product y has a greater profit per unit, it is more profitable to sell more units of y than x. Therefore, as the number of units of y sold increases, the increase in profit will be greater than the increase in profit from selling more units of x. This means the slope of the objective function will be negative, indicating that as the number of units of x sold increases, the number of units of y sold will decrease. The slope can be calculated as: (change in profit)/(change in units). For every unit of y sold, the increase in profit is $10, while for every unit of x sold, the increase in profit is $5. Therefore, the slope is:

(change in profit)/(change in units) = ($10 - $5)/(1) = $5

Since the slope is positive, we know that the number of units of x sold will also increase as the number of units of y sold increases. Therefore, the best choice would be to sell a combination of x and y that maximizes total profit, while keeping in mind that selling more units of y will contribute more to this total profit.

Question 4

In using Excel to solve linear programming problems,the changing cells represent the:
A)value of the objective function
B)constraints
C)decision variables
D)total cost of the model

Accepted Answer

The changing cells in linear programming represent the decision variables, which are the variables that we want to optimize in order to minimize or maximize the objective function. The objective function and constraints are fixed and do not change with the optimization process. The total cost of the model may be related to the decision variables, but it is not the same as the changing cells.

Question 5

A linear programming problem with only decision variable(s)can be solved by a graphical solution method.
A)1
B)2
C)3
D)4

Accepted Answer

Graphical solution method is only applicable when there is only one or two decision variable(s) in a linear programming problem. Hence, only choice 1 is the best option.

Question 6

The solution of a linear programming problem using Microsoft Excel typically involves the following three stages:
A)formulating the problem,invoking Solver,and sensitivity analysis
B)formulating the problem,graphing the problem,and sensitivity analysis
C)the changing cells,the target cells,and the constraints
D)the inputs,the changing cells,and the outputs

Accepted Answer

The three stages of solving a linear programming problem in Microsoft Excel are: 
1. Formulating the problem - this involves identifying the decision variables, objective function, and constraints. 
2. Invoking Solver - this is the Excel tool used for solving optimization problems. It works by adjusting the values of the decision variables until the optimal solution is found. 
3. Sensitivity analysis - this involves analyzing the impact of changes to the input values and constraints on the optimal solution. Therefore, choice A is the best option since it includes all three stages.

Question 7

The most important solution method for linear programming problems is known as the:
A)spreadsheet method
B)solution mix method
C)complex method
D)simplex method

Accepted Answer

The simplex method is the most important and widely used method for solving linear programming problems. It is efficient, reliable, and provides optimal solutions to problems with many variables and constraints. The other options listed are either incorrect (spreadsheet method) or not commonly used (solution mix method, complex method).

Question 8

The equation of the line representing the constraint  is:
A) 
B) 
C) 
D)

Accepted Answer

The answer of The equation of the line representing the...

Question 9

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit.This type of problem is referred to as the:
A)product mix problem
B)production problem
C)product/process problem
D)product scheduling problem

Accepted Answer

The prototype linear programming problem described in the question is specifically called the product mix problem. This is because the goal is to determine the optimal combination or mix of products to produce in order to maximize profit. Option B (production problem) is too broad and could refer to any problem related to producing goods or services. Option C (product/process problem) is not an established term in linear programming and is not specific enough to the problem described. Option D (product scheduling problem) refers to a different type of problem where the goal is to determine the best schedule for producing a set of products given certain constraints, which is not the case in the prototype problem presented here.

Question 10

Every linear programming problem involves optimizing a:
A)linear regression model subject to several linear constraints
B)linear function subject to several linear constraints
C)linear function subject to several non-linear constraints
D)non-linear function subject to several linear constraints

Accepted Answer

Linear programming involves optimizing a linear objective function subject to linear constraints.

Question 11

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y.An algebraic formulation of these constraints is:
A) 
B) 
C) 
D)

Accepted Answer

The answer of Suppose a firm must at least meet...

Question 12

In an optimization model,there can only be one:
A)decision variable
B)constraint
C)objective function
D)shadow price

Accepted Answer

There can be multiple decision variables and constraints in an optimization model, but there can only be one objective function. The objective function is the function that needs to be optimized in the model. Shadow price is a variable that represents the change in the objective function due to a unit change in the constraints. Thus, there can be multiple shadow prices in the model.

Question 13

In most cases in solving linear programming problems,we want the decision variables to be:
A)equal to zero
B)nonnegative
C)nonpositive
D)All of these options

Accepted Answer

In almost all cases of solving linear programming problems, we want the decision variables to be nonnegative since negative values do not make sense in real-world applications. In other words, it is not possible to have negative answers for production amounts, sales, or other quantities. However, decision variables do not necessarily have to be equal to zero or nonpositive.

Question 14

Linear programming is a subset of a larger class of models called:
A)mathematical programming models
B)mathematical optimality models
C)linear regression models
D)linear simplex model

Accepted Answer

Linear programming is a type of mathematical programming model that involves maximizing or minimizing a linear objective function subject to linear constraints. Linear programming is a widely used mathematical optimization technique in business and economics for allocating resources efficiently. The other options (B, C, and D) do not accurately describe the relationship between linear programming and the broader class of mathematical models.

Question 15

In using Excel to solve linear programming problems,the target cell represents the:
A)value of the objective function
B)constraints
C)decision variables
D)total cost of the model

Accepted Answer

The target cell in Excel represents the value of the objective function in linear programming problems. It is the cell that is being optimized, whether it's maximizing profits, minimizing costs, or achieving a specific goal. The constraints and decision variables are represented in other cells in the worksheet.

Question 16

All optimization problems have:
A)an objective function and decision variables
B)an objective function and constraints
C)decision variables and constraints
D)an objective function,decision variables and constraints

Accepted Answer

The answer of All optimization problems have:
A)an objective function and...

Question 17

The term nonnegativity refers to the condition where:
A)the objective function cannot be less that zero
B)the decision variables cannot be less than zero
C)the right hand side of the constraints cannot be greater then zero
D)the reduced cost cannot be less than zero

Accepted Answer

Nonnegativity implies that the decision variables cannot take negative values. This is because in many practical situations negative values do not make sense. For example, the number of employees hired cannot be negative, or the amount of material used in manufacturing cannot be negative. Therefore, choice B is the correct answer. Choice A refers to the nonnegativity of the objective function, which is usually not a condition for linear programming problems. Choice C refers to the sign restrictions on the right-hand side of the constraints, which may or may not be nonnegative. Choice D refers to the optimality conditions for linear programming, which may or may not involve nonnegativity.

Question 18

Suppose a liquor store sells beer for a net profit of $1 per unit and wine for a net profit of $2 per unit.Let x equal the amount of beer sold and y equal the amount of wine sold.An algebraic formulation of the profit function is:
A) 
B) 
C) 
D)

Accepted Answer

The answer of Suppose a liquor store sells beer for...

Question 19

The feasible region in all linear programming problems is bounded by:
A)corner points
B)hyperplanes
C)an objective line
D)all of these options

Accepted Answer

The feasible region in linear programming problems is bounded by hyperplanes, which are geometric representations of the constraints in the problem. These hyperplanes are essentially the lines (in two dimensions), planes (in three dimensions), or higher-dimensional analogs that define the limits of the feasible region. Corner points and an objective line are elements related to the feasible region and the optimization process, but they do not bound the feasible region themselves.

Question 20

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the:
A)optimal region
B)feasible region
C)constrained region
D)logical region

Accepted Answer

The feasible region is the set of points that satisfy all constraints, and it is where the optimal solution will exist. The other options (optimal region, constrained region, logical region) are not commonly used terms in linear programming.

Quiz 13: Introduction to Optimization Modeling

The optimal solution to any linear programming model is:

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is:

Suppose a company sells two different products,x and y,for net profits of $5 per unit and $10 per unit,respectively.The slope of the line representing the objective function is:

In using Excel to solve linear programming problems,the changing cells represent the:

A linear programming problem with only decision variable(s) can be solved by a graphical solution method.

The solution of a linear programming problem using Microsoft Excel typically involves the following three stages:

The most important solution method for linear programming problems is known as the:

The equation of the line representing the constraint is:

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit.This type of problem is referred to as the:

Every linear programming problem involves optimizing a:

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y.An algebraic formulation of these constraints is:

In an optimization model,there can only be one:

In most cases in solving linear programming problems,we want the decision variables to be:

Linear programming is a subset of a larger class of models called:

In using Excel to solve linear programming problems,the target cell represents the:

All optimization problems have:

The term nonnegativity refers to the condition where:

Suppose a liquor store sells beer for a net profit of $1 per unit and wine for a net profit of $2 per unit.Let x equal the amount of beer sold and y equal the amount of wine sold.An algebraic formulation of the profit function is:

The feasible region in all linear programming problems is bounded by:

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the: