Question 1

According to the mathematical theory underlying LP problems,the optimal solution to an LP problem will occur at ______.

Accepted Answer

A) one of the corner points of the feasible space 
B) all of the corner points of the feasible space 
C) any point inside the feasible space 
D) any point outside the feasible space 
A) one of the corner points of the feasible space 
B) all of the corner points of the feasible space 
C) any point inside the feasible space 
D) any point outside the feasible space A

Question 2

Which of the following is a method in which parallel cost lines are plotted in the LP graphical solution approach to determine the least cost solution to LP problems with cost minimization objective?

Accepted Answer

A) graphical method 
B) corner point solution method 
C) iso-cost line method 
D) iso-profit line method 
A) graphical method 
B) corner point solution method 
C) iso-cost line method 
D) iso-profit line method C

Question 3

Which of the following is a method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective?

Accepted Answer

A) graphical method 
B) corner point solution method 
C) iso-cost line method 
D) iso-profit line method 
A) graphical method 
B) corner point solution method 
C) iso-cost line method 
D) iso-profit line method D

Question 4

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements are shown here. $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Beans }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l } 
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \begin{array} { l } 
\text { Calories in units per } \
\text { pound }
\end{array} & 3 & 9 & 18 \
\hline
\end{array}$$ At the optimum solution,what is the number of pounds of kidney beans included in the diet?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
A) 1 
B) 2 
C) 3 
D) 4

Question 5

Consider the portion of the sensitivity analysis report that follows.Decreasing the right-hand constraint Calcium by 1 unit (30 to 29)will result in which of the following? $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Constraints } & & & & & & \
\hline \text { Cell } & \text { Name } & \text { Final Value } & \begin{array} { l } 
\text { Shadow } \
\text { Price }
\end{array} & \begin{array} { l } 
\text { Constrant } \
\text { RH. Side }
\end{array} & \begin{array} { l } 
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array} { l } 
\text { Allowable } \
\text { Decrease }
\end{array} \
\hline \$ \mathrm { H } \$ 5 & \text { Calcium } & 30 & 0 & 30 & 0 & 1 \mathrm { E } + 30 \
\hline \$ \mathrm { H } \$ 5 & \text { Protein } & 40 & 0.025 & 40 & 20 & 0 \
\hline \$ \mathrm { H } \$ 7 & \text { Calories } & 18 & 0.25 & 18 & 0 & 6 \
\hline
\end{array}$$

Accepted Answer

A) decrease cost by $0.225 
B) does not affect cost 
C) increase cost by $0.225 
D) increase cost by $0.025 
A) decrease cost by $0.225 
B) does not affect cost 
C) increase cost by $0.225 
D) increase cost by $0.025

Question 6

A school is trying to determine a nutritional diet to feed its students.The objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements,are shown here.Let K and T be the number pounds of kidney beans and tofu to be purchased.Determine the objective function. $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Besns }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l } 
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \begin{array} { l } 
\text { Protein in units per } \
\text { pound } 
\end{array} & 10 & 10 & 40 \
\hline\begin{array} { l } 
\text { Calories in units per } \
\text { pound }
  \end{array} & \mathbf { 3 } & 9 & 18 \
\hline
\end{array}$$

Accepted Answer

A) Minimize cost = $0.90K + $1.50T 
B) Minimize cost = 1K + 1T 
C) Maximize cost = $0.90K + $1.50T 
D) Maximize cost = $1.00K + $1.50T 
A) Minimize cost = $0.90K + $1.50T 
B) Minimize cost = 1K + 1T 
C) Maximize cost = $0.90K + $1.50T 
D) Maximize cost = $1.00K + $1.50T

Question 7

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements are shown here. $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Beans }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l } 
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \begin{array} { l } 
\text { Calories in units per } \
\text { pound }
\end{array} & 3 & 9 & 18 \
\hline
\end{array}$$ At the optimum solution,what is the number of pounds of tofu included in the diet?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
A) 1 
B) 2 
C) 3 
D) 4

Question 8

Which of the following is NOT one of the features of a linear programming problem?

Accepted Answer

A) decision variables 
B) consequences 
C) constraints 
D) linearity 
A) decision variables 
B) consequences 
C) constraints 
D) linearity

Question 9

Which of the following methods do we use in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective?

Accepted Answer

A) iso-cost line method 
B) sensitivity analysis method 
C) simplex method 
D) iso-profit line method 
A) iso-cost line method 
B) sensitivity analysis method 
C) simplex method 
D) iso-profit line method

Question 10

ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine the objective function for the LP formulation.

Accepted Answer

A) Maximize profit = $11 * (Number of shirts to be produced + Number of pairs of pants to be produced) 
B) Maximize profit = $5 * Number of shirts to be produced 
C) Maximize profit = $6 * Number of pairs of pants to be produced 
D) Maximize profit = ($5 * Number of shirts to be produced)+ ($6 * Number of pairs of pants to be produced) 
A) Maximize profit = $11 * (Number of shirts to be produced + Number of pairs of pants to be produced) 
B) Maximize profit = $5 * Number of shirts to be produced 
C) Maximize profit = $6 * Number of pairs of pants to be produced 
D) Maximize profit = ($5 * Number of shirts to be produced)+ ($6 * Number of pairs of pants to be produced)

Question 11

In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the amount of nitrogen from the Nitro Plus brand?

Accepted Answer

A) 11.45 
B) 12.80 
C) 17.65 
D) 11.55 
A) 11.45 
B) 12.80 
C) 17.65 
D) 11.55

Question 12

______ in linear programming are an alternative course of action-for example,determining the number of shipping routes for transporting goods from the available alternative choices.

Accepted Answer

A) Decision variables 
B) Consequences 
C) Constraints 
D) Linearity 
A) Decision variables 
B) Consequences 
C) Constraints 
D) Linearity

Question 13

Using linear programming (LP)to determine the optimum investment portfolio that will achieve certain returns while minimizing investment risks is an example of applying LP to solving ______ problems.

Accepted Answer

A) financial planning 
B) production planning 
C) assignment 
D) transportation 
A) financial planning 
B) production planning 
C) assignment 
D) transportation

Question 14

Consider the sensitivity analysis report that follows.The shadow price of $0.6 is valid as long as the right-hand constraint of 240 is within the range of ______. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Cell } & \text { Name } & \begin{array} { l } 
\text { Final } \
\text { Value }
\end{array} & \begin{array} { l } 
\text { Shadow } \
\text { Price }
\end{array} & \begin{array} { l } 
\text { Constraint } \
R \mathrm { H } \text {. Side }
\end{array} & \begin{array} { l } 
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array} { l } 
\text { Alowable } \
\text { Decrease }
\end{array} \
\hline \$ 1 \$ 7 & \begin{array} { l } 
< = \
\text { Usage }
\end{array} & 240 & 0.6 & 240 & 210 & 40 \
\hline \$ 1 \$ 8 & \begin{array} { l } 
< = \
\text { Usage }
\end{array} & 150 & 3.2 & 150 & 30 & 70 \
\hline
\end{array}$$

Accepted Answer

A) 200 to 450 
B) 150 to 240 
C) 200 to 300 
D) 40 to 210 
A) 200 to 450 
B) 150 to 240 
C) 200 to 300 
D) 40 to 210

Question 15

Maureen,hospital administrator for Trinity Hospital,would like to set up a work schedule for the hospital's nurses.Each nurse will work for 8 consecutive hours.The minimum number of nurses needed in each of six 4-hour time intervals is shown in the following table.At the optimal staffing level,how many nurses will start their shift at 8a.m.? $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Time interval } & 00 - 04 & 04 - 08 & 08 - 12 & 12 - 16 & 16 - 20 & 20 - 24 \
\hline \begin{array} { l } 
\text { Minimum number } \
\text { of nurses required }
\end{array} & 7 & 8 & 22 & 26 & 18 & 12 \
\hline
\end{array}$$

Accepted Answer

A) 21 
B) 4 
C) 12 
D) 8 
A) 21 
B) 4 
C) 12 
D) 8

Question 16

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements are shown here. $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Beans }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l } 
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \begin{array} { l } 
\text { Calories in units per } \
\text { pound }
\end{array} & 3 & 9 & 18 \
\hline
\end{array}$$ At the optimum solution,what is the cost of the nutritional diet?

Accepted Answer

A) $4.20 
B) $3.55 
C) $7.30 
D) $8.25 
A) $4.20 
B) $3.55 
C) $7.30 
D) $8.25

Question 17

Consider the portion of the sensitivity analysis report that follows.Decreasing the right-hand side constraint by 1 unit for $I$8 (from 150 to 149)will result in which of the following? $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Cell } & \text { Name } & \begin{array} { l } 
\text { Final } \
\text { Value }
\end{array} & \begin{array} { l } 
\text { Shadow } \
\text { Price }
\end{array} & \begin{array} { l } 
\text { Constraint } \
R \mathrm { H } \text {. Side }
\end{array} & \begin{array} { l } 
\text { Allowable } \
\text { Increase }
\end{array} & \begin{array} { l } 
\text { Alowable } \
\text { Decrease }
\end{array} \
\hline \$ 1 \$ 7 & \begin{array} { l } 
< = \
\text { Usage }
\end{array} & 240 & 0.6 & 240 & 210 & 40 \
\hline \$ 1 \$ 8 & \begin{array} { l } 
< = \
\text { Usage }
\end{array} & 150 & 3.2 & 150 & 30 & 70 \
\hline
\end{array}$$

Accepted Answer

A) decrease the profit by $0.6 
B) increase the profit by $3.2 
C) increase the profit by $0.6 
D) decrease the profit by $3.2 
A) decrease the profit by $0.6 
B) increase the profit by $3.2 
C) increase the profit by $0.6 
D) decrease the profit by $3.2

Question 18

Which of the following is a mathematical modeling technique that managers can use in making decisions that involve optimizing an objective,subject to constraints?

Accepted Answer

A) optimization 
B) estimation 
C) linear programming 
D) transportation model 
A) optimization 
B) estimation 
C) linear programming 
D) transportation model

Question 19

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements are shown here. $$\begin{array} { | l | l | l | l | } 
\hline \text { Nutrient } & \begin{array} { l } 
\text { Kidney } \
\text { Beans }
\end{array} & \text { Tofu } & \begin{array} { l } 
\text { Minimum Daily } \
\text { Requirement }
\end{array} \
\hline \text { Cost per pound } & \$ 0.90 & \$ 1.50 & \
\hline \begin{array} { l } 
\text { Calcium in units per } \
\text { pound }
\end{array} & 15 & 6 & 30 \
\hline \text { Protein in units per pound } & 10 & 10 & 40 \
\hline \begin{array} { l } 
\text { Calories in units per } \
\text { pound }
\end{array} & 3 & 9 & 18 \
\hline
\end{array}$$ At the optimum solution,which of the following statements is true?

Accepted Answer

A) The number of calories contributed by tofu is equal to that provided by kidney beans. 
B) The number of calories contributed by tofu is less than that provided by kidney beans. 
C) The number of calories contributed by tofu is more than that provided by kidney beans. 
D) The number of calories contributed by tofu is double that provided by kidney beans. 
A) The number of calories contributed by tofu is equal to that provided by kidney beans. 
B) The number of calories contributed by tofu is less than that provided by kidney beans. 
C) The number of calories contributed by tofu is more than that provided by kidney beans. 
D) The number of calories contributed by tofu is double that provided by kidney beans.

Question 20

The graphical method is appropriate for solving simple linear programming problems involving ______ decision variables.

Accepted Answer

A) one 
B) two 
C) three 
D) four 
A) one 
B) two 
C) three 
D) four

According to the mathematical theory underlying LP problems,the optimal solution to an LP problem will occur at ______.

Which of the following is a method in which parallel cost lines are plotted in the LP graphical solution approach to determine the least cost solution to LP problems with cost minimization objective?

Which of the following is a method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective?

Which of the following is NOT one of the features of a linear programming problem?

Which of the following methods do we use in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective?

______ in linear programming are an alternative course of action-for example,determining the number of shipping routes for transporting goods from the available alternative choices.

Using linear programming (LP)to determine the optimum investment portfolio that will achieve certain returns while minimizing investment risks is an example of applying LP to solving ______ problems.

Which of the following is a mathematical modeling technique that managers can use in making decisions that involve optimizing an objective,subject to constraints?

The graphical method is appropriate for solving simple linear programming problems involving ______ decision variables.

Introduction to Managing Global Operations and Supply Chains

Operations and Supply Chain Strategies

Project Management

Supplement: Project Management

Product and Service Innovations

Supplement: Reliability

Managing for Quality

Quality Improvement and Control Tools

Capacity Planning

Supply Chain Design and Location Planning

Process Design and Layout Planning

Supplement: Tools for Analyzing, Designing, and Selecting Processes and Layouts

Supplier Management

Logistics Management

Demand Management and Customer Service

Demand Forecasting Methods

Lean Operations and Supply Chains

Inventory Management

Inventory Control Models

Sales and Operations Planning

Master Scheduling and Material Requirements Planning

Supplement: Capacity Requirements Planning, MRP II, ERP, and DRP

Detailed Scheduling

The Transportation Models

Waiting Line Models

Simulation

Learning Curves

Decision-Making Tools

Filters

Exam 24: Linear Programming

According to the mathematical theory underlying LP problems,the optimal solution to an LP problem will occur at ______.

Which of the following is a method in which parallel cost lines are plotted in the LP graphical solution approach to determine the least cost solution to LP problems with cost minimization objective?

Which of the following is a method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective?

Which of the following is NOT one of the features of a linear programming problem?

Which of the following methods do we use in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective?

______ in linear programming are an alternative course of action-for example,determining the number of shipping routes for transporting goods from the available alternative choices.

Using linear programming (LP)to determine the optimum investment portfolio that will achieve certain returns while minimizing investment risks is an example of applying LP to solving ______ problems.

Which of the following is a mathematical modeling technique that managers can use in making decisions that involve optimizing an objective,subject to constraints?

The graphical method is appropriate for solving simple linear programming problems involving ______ decision variables.

Introduction to Managing Global Operations and Supply Chains

Operations and Supply Chain Strategies

Project Management

Supplement: Project Management

Product and Service Innovations

Supplement: Reliability

Managing for Quality

Quality Improvement and Control Tools

Capacity Planning

Supply Chain Design and Location Planning

Process Design and Layout Planning

Supplement: Tools for Analyzing, Designing, and Selecting Processes and Layouts

Supplier Management

Logistics Management

Demand Management and Customer Service

Demand Forecasting Methods

Lean Operations and Supply Chains

Inventory Management

Inventory Control Models

Sales and Operations Planning

Master Scheduling and Material Requirements Planning

Supplement: Capacity Requirements Planning, MRP II, ERP, and DRP

Detailed Scheduling

The Transportation Models

Waiting Line Models

Simulation

Learning Curves

Decision-Making Tools

Filters