Question 1

A company has normal capacity for 2,500 units a month. If, x₁₁ and x₂₁ represent the production decisions variables, which of the following equations represents the occurrence of change? A) x₁₁ + x₂₁ − 2500 B) x₁₁ − x₂₁ − 2500 C) x₁₂ − x₂₁ − 2500 D) x₁₂ + x₂₁ − 2500

Accepted Answer

The equation x₁₁ + x₂₁ − 2500 represents the total production from both variables subtracted by the normal capacity, indicating the occurrence of change in production relative to normal capacity.

Question 2

Excel Solver can handle basic linear programming but not the special transportation problem.

Accepted Answer

Excel Solver can handle basic linear programming but not the special transportation problem.

Question 3

If a company has a demand of 1,600 units for the month of May and a beginning of 900 units, and if X_m = production in May and L_m = the number of lost sales in May, which of the following equations represents the material-balance constraint? A) X_m - I_m + 900 + L_m = 1,600 B) X_m + I_m - 900 + L_m = 1,600 C) X_m - I_m + 900 - L_m = 1,600 D) -X_m - I_m + 900 - L_m = 1,600

Accepted Answer

The material-balance constraint states that the beginning inventory plus production minus the ending inventory equals demand plus lost sales. In this case, the beginning inventory is 900 units, the demand is 1,600 units, and the lost sales are L_m units. Therefore, the material-balance constraint is:X_m - I_m + 900 + L_m = 1,600

Question 4

Which of the following factors would generally NOT be part of a linear programming model for blending?
A) Revenue
B) Cost
C) Product/component specifications
D) Supply = demand

Accepted Answer

Supply=demand is not typically a factor in a linear programming model for blending, as it is more commonly considered in models for production and inventory management. The other factors listed (revenue, cost, and product/component specifications) are all commonly included in a linear programming model for blending.

Question 5

The total project cost can be minimized by minimizing crash costs.

Accepted Answer

Crash costs refer to the additional expenses incurred when a project is accelerated to meet a shorter timeframe or deadline. By minimizing the need for crashing, the total project cost can be reduced as there would be fewer additional expenses.

Question 6

The constraint x₁ and x₂ $\ge$ 0 refers to: A) feasibility. B) maximization. C) binding. D) nonnegativity.

Accepted Answer

The constraint described involves variables and their relationships, indicating that all variables must be greater than or equal to zero. This is a fundamental requirement in linear programming and optimization problems, ensuring that solutions are realistic and practical, hence it refers to nonnegativity.

Question 7

Any particular combination of decision variables is referred to as a(n) _____.
A) objective
B) solution
C) constraint
D) coefficient

Accepted Answer

A combination of decision variables that satisfies all the constraints and optimizes the objective function is called a solution. The other options are not correct definitions of a combination of decision variables.

Question 8

A company is considering a rate change, either an increase or a decrease in production, where X_t = production in a time period; R_t = increase in production rate from Period t−1 to Period t; D_t = decrease in production rate from Period t−1 to Period t. Which of the following is correct? A) X_t − X_{t - 1} = D_t − R_t B) X_{t - 1} − X_t = D_t − R_t C) X_{t - 1} − X_t = R_t − D_t D) X_t − X_{t - 1} = R_t − D_t

Accepted Answer

X_t − X_{t - 1} represents the change in production from Period t−1 to Period t. D_t − R_t represents the net change in production rate from Period t−1 to Period t. Therefore, the correct equation is X_t − X_{t - 1} = R_t − D_t.

Question 9

Since price is usually set by market conditions, the blending problem's use of linear programming attempts to meet the demand at a minimum cost.

Accepted Answer

This statement is true. Linear programming is a tool used to optimize a process or system, and in the blending problem, it is used to determine the optimal mix of ingredients to meet the demand at the lowest cost possible, given the market conditions.

Question 10

For linear programming to work for project crashing decisions, a dummy activity is needed at the beginning of the project, with a duration of zero (0) time.

Accepted Answer

In linear programming for project crashing, dummy activities are used to represent precedence relationships between tasks, not necessarily at the beginning of the project, and their duration is not relevant to their purpose.

Question 11

Deciding on how much of each grade of gasoline to produce is an example of the linear programming model for blending applications.

Accepted Answer

Linear programming is a mathematical optimization technique used to determine the best outcome from a given set of linear relationships. Blending applications, such as gasoline production, involve determining the optimal combination of different grades of gasoline to produce based on factors such as cost and demand. Therefore, deciding on how much of each grade of gasoline to produce is an example of the linear programming model for blending applications.

Question 12

The term 'programming' is used in linear programming because these models find the best 'program' or course of action to follow.

Accepted Answer

Linear programming models aim to find the optimum plan or course of action to follow, which is commonly referred to as a 'program'. Thus, the term 'programming' is used in linear programming to reflect this objective.

Question 13

The constraint that requires the ending inventory from previous month plus current production minus ending inventory of this month equals this month's demand is known as a demand requirement.

Accepted Answer

This statement describes the equation for inventory balance, which is a key constraint in inventory management. It ensures that the amount of inventory available at the beginning of the month plus the amount produced during the month is sufficient to meet customer demand, while accounting for any inventory that remains at the end of the month. This equation is also known as the inventory balance equation or the inventory continuity equation.

Question 14

If R_m = increase in the total production level during month 'm' compared to month m-1 and D_m = decrease in the total production level during month 'm' compared to month m-1, which of the following statements can be correct? A) R_m = D_m = 0. B) Both R_m and D_m are positive. C) Both R_m and D_marenegative. D) One variable can be positive and the other negative.

Accepted Answer

Both R_m and D_m represent changes in production levels, therefore one variable can be positive (indicating an increase in production) and the other negative (indicating a decrease in production). Option A is incorrect because it assumes there are no changes in production. Option B is incorrect because it assumes there are only increases in production. Option C is incorrect because it assumes there are only decreases in production.

Question 15

If a single variable is used to represent the change in production level, only positive changes would be permitted, because of the nonnegativity requirement.

Accepted Answer

A nonnegativity requirement means that the variable can only take on non-negative values. This means that only positive changes in production level would be permitted, as negative changes would result in negative values for the variable.

Question 16

Which of the following factors would generally NOT be part of a linear programming model for production scheduling?
A) Fluctuations in production
B) Inventory levels
C) Waiting time probability distributions
D) Storage capacity

Accepted Answer

Linear programming models for production scheduling typically focus on optimizing the allocation of resources to achieve a specific objective, such as maximizing profits or minimizing costs. Factors such as fluctuations in production, inventory levels, and storage capacity are relevant to this objective and would typically be included in the model. However, waiting time probability distributions are not typically included as they are more relevant to queuing models for analyzing wait times in service systems.

Question 17

Constant terms in the objective function are called objective function _____.
A) variables
B) decisions
C) coefficients
D) constraints

Accepted Answer

Constant terms in the objective function are called objective function coefficients. These coefficients represent the values that are multiplied by decision variables in the objective function to determine the overall value of the objective function. Variables and decisions refer to the choices that the decision maker must make in the optimization problem, while constraints are the limitations or restrictions on those choices.

Question 18

Solutions to a linear programming model that satisfy all constraints are referred to as optimal.

Accepted Answer

Solutions that satisfy all constraints are referred to as feasible solutions. The optimal solution is the feasible solution that results in the best value (maximum or minimum) of the objective function.

Question 19

In production scheduling, (ending inventory from the previous month) + (current production)-(ending inventory this month) = _____.
A) production rate change
B) this month's demand
C) amount of overtime/undertime
D) next month's inventory

Accepted Answer

This equation calculates the amount of goods needed to meet this month's demand, taking into account the inventory left over from the previous month and the inventory that will remain at the end of this month.

Question 20

The transportation problem is a special type of linear programming that arises in planning the distribution of goods and services from only one supply point to several demand locations.

Accepted Answer

The transportation problem is a type of linear programming problem that involves distributing goods and services from multiple supply points to multiple demand locations, not just from one supply point.

Quiz 17: Appendix: Modeling Using Linear Programming

A company has normal capacity for 2,500 units a month. If, x₁₁ and x₂₁ represent the production decisions variables, which of the following equations represents the occurrence of change?

Excel Solver can handle basic linear programming but not the special transportation problem.

If a company has a demand of 1,600 units for the month of May and a beginning of 900 units, and if X_m = production in May and L_m = the number of lost sales in May, which of the following equations represents the material-balance constraint?

Which of the following factors would generally NOT be part of a linear programming model for blending?

The total project cost can be minimized by minimizing crash costs.

The constraint x₁ and x₂ $\ge$ 0 refers to:

Any particular combination of decision variables is referred to as a(n) _____.

A company is considering a rate change, either an increase or a decrease in production, where X_t = production in a time period; R_t = increase in production rate from Period t−1 to Period t; D_t = decrease in production rate from Period t−1 to Period t. Which of the following is correct?

Since price is usually set by market conditions, the blending problem's use of linear programming attempts to meet the demand at a minimum cost.

For linear programming to work for project crashing decisions, a dummy activity is needed at the beginning of the project, with a duration of zero (0) time.

Deciding on how much of each grade of gasoline to produce is an example of the linear programming model for blending applications.

The term 'programming' is used in linear programming because these models find the best 'program' or course of action to follow.

The constraint that requires the ending inventory from previous month plus current production minus ending inventory of this month equals this month's demand is known as a demand requirement.

If R_m = increase in the total production level during month 'm' compared to month m-1 and D_m = decrease in the total production level during month 'm' compared to month m-1, which of the following statements can be correct?

If a single variable is used to represent the change in production level, only positive changes would be permitted, because of the nonnegativity requirement.

Which of the following factors would generally NOT be part of a linear programming model for production scheduling?

Constant terms in the objective function are called objective function _____.

Solutions to a linear programming model that satisfy all constraints are referred to as optimal.

In production scheduling, (ending inventory from the previous month) + (current production) -(ending inventory this month) = _____.

The transportation problem is a special type of linear programming that arises in planning the distribution of goods and services from only one supply point to several demand locations.

Quiz 17: Appendix: Modeling Using Linear Programming

A company has normal capacity for 2,500 units a month. If, x11 and x21 represent the production decisions variables, which of the following equations represents the occurrence of change?

Excel Solver can handle basic linear programming but not the special transportation problem.

If a company has a demand of 1,600 units for the month of May and a beginning of 900 units, and if Xm = production in May and Lm = the number of lost sales in May, which of the following equations represents the material-balance constraint?

Which of the following factors would generally NOT be part of a linear programming model for blending?

The total project cost can be minimized by minimizing crash costs.

The constraint x1 and x2 ≥\ge≥ 0 refers to:

Any particular combination of decision variables is referred to as a(n) _____.

A company is considering a rate change, either an increase or a decrease in production, where Xt = production in a time period; Rt = increase in production rate from Period t−1 to Period t; Dt = decrease in production rate from Period t−1 to Period t. Which of the following is correct?

Since price is usually set by market conditions, the blending problem's use of linear programming attempts to meet the demand at a minimum cost.

For linear programming to work for project crashing decisions, a dummy activity is needed at the beginning of the project, with a duration of zero (0) time.

Deciding on how much of each grade of gasoline to produce is an example of the linear programming model for blending applications.

The term 'programming' is used in linear programming because these models find the best 'program' or course of action to follow.

The constraint that requires the ending inventory from previous month plus current production minus ending inventory of this month equals this month's demand is known as a demand requirement.

If Rm = increase in the total production level during month 'm' compared to month m-1 and Dm = decrease in the total production level during month 'm' compared to month m-1, which of the following statements can be correct?

If a single variable is used to represent the change in production level, only positive changes would be permitted, because of the nonnegativity requirement.

Which of the following factors would generally NOT be part of a linear programming model for production scheduling?

Constant terms in the objective function are called objective function _____.

Solutions to a linear programming model that satisfy all constraints are referred to as optimal.

In production scheduling, (ending inventory from the previous month) + (current production) -(ending inventory this month) = _____.

The transportation problem is a special type of linear programming that arises in planning the distribution of goods and services from only one supply point to several demand locations.

A company has normal capacity for 2,500 units a month. If, x₁₁ and x₂₁ represent the production decisions variables, which of the following equations represents the occurrence of change?

If a company has a demand of 1,600 units for the month of May and a beginning of 900 units, and if X_m = production in May and L_m = the number of lost sales in May, which of the following equations represents the material-balance constraint?

The constraint x₁ and x₂ $\ge$ 0 refers to:

A company is considering a rate change, either an increase or a decrease in production, where X_t = production in a time period; R_t = increase in production rate from Period t−1 to Period t; D_t = decrease in production rate from Period t−1 to Period t. Which of the following is correct?

If R_m = increase in the total production level during month 'm' compared to month m-1 and D_m = decrease in the total production level during month 'm' compared to month m-1, which of the following statements can be correct?