MGMT 630 – 851 and 853 Mid Term Exam 2 Sample Multiple Choice Questions
Sample Multiple Choice Questions (includes Chapters 7, 8, 9 and 10 only)
Please do use the lecture notes and textbook to study for the Exam. Please do feel free to bring your questions to the Live WebEx Sessions.
Multiple Choice Questions for Chapter 7 (Introduction to Linear Programming Models)
1. Assumptions of linear programming include
A) linearity
B) additivity
C) divisibility
D) certainty
E) all of the above
2. Divisibility assumption in linear programming implies
A) resources can be divided among products
B) products can be divided among customers
C) decision variables may take on integer values
D) decision variables may take on fractional values
3. Additivity assumption in linear programming implies
A) resources can be added together to generate products
B) products can be added at any time
C) resource usage for each level of decision variable can be added up to get total usage
D) total profit for each decision variable can be added up to get total profit for the model
E) C and D
4. Per unit contribution for a new cooker goes down by 5% as a salesman tries harder and harder to sell the cooker. For this situation
A) a linear programming model will be appropriate
B) an integer linear programming will be appropriate
C) an integer linear program may be appropriate
D) a linear program will not be appropriate
E) none of the above
5. Consider the following constraints and choose the correct answer:
Constraint A: Constraint B:
A) constraint A can be used in a linear program
B) constraint B can be used in a linear program
C) neither can be used in a linear program
D) both may be used in a linear program
E) both may be used in an integer linear program, but not in linear program
6. Consider the following constraints and choose the correct answer:
Constraint A: Constraint B:
A) constraint A can be used in a linear program
B) constraint B can be used in a linear program
C) neither can be used in a linear program
D) both may be used in a linear program
E) both may be used in an integer linear program, but not in a linear program
7. Certainty assumption in linear programming implies
A) available resources, profit and other coefficients are known with certainty
B) all constraints on the system have been included in the model.
C) A and B
D) neither A nor B
E) the right problem has been formulated with certainty
8. XYZ Inc. produces two types of paper towels—regular and super-soaker. Marketing has imposed a constraint that the total monthly production of regular should be no more than twice the monthly production of super-soakers. Let be the number of units of regular produced per month and the number of units of super-soaker produced per month. The appropriate constraint/s will be
A)
B)
C)
D)
E)
9. XYZ Inc. produces two types of paper towels—regular and super-soaker. Manufacturing has imposed a constraint that the total monthly production of regular should be at least as many as the monthly production of super-soakers. Let be the number of units of regular produced per month and the number of units of super-soaker produced per month, the appropriate constraint/s will be
A)
B)
C)
D)
E)
10. XYZ Inc. produces two types of paper towels—regular and super-soaker. Manufacturing has imposed a constraint that the total monthly production of regular and super-soaker should be in the ratio of 2:3. Let be the number of units of regular produced per month and the number of units of super-soaker produced per month. The appropriate constraint/s will be
A)
B)
C)
D)
E) C or D, since they both mean the same thing
11. XYZ Inc. produces two types of paper towels—regular and super-soaker. Regular uses 2 units of recycled paper per unit of production, and super-soaker uses 3 units of recycled paper per unit of production. The total amount of recycled paper available per month is 10,000. Let be the number of units of regular produced per month and the number of units of super-soaker produced per month. The appropriate constraint/s will be
A)
B)
C)
D)
E) A, B, and C
12. XYZ Inc. produces two types of paper towels—regular and super-soaker. Regular uses 2 units of recycled paper per unit of production, and super-soaker uses 3 units of recycled paper per unit of production. The total amount of recycled paper available per month is 10,000. They also have a binding contract to use at least 8,000 units of recycled paper per month with a local pollution control organization. Let be the number of units of regular produced per month and the number of units of super-soaker produced per month, the appropriate constraint/s will be
A)
B)
C)
D) A or B but not both
E) A and B
13. XYZ Inc. produces two types of printers—regular and high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. The total amount of recycled plastic available per month is 5,000. A critical machine is needed to manufacture the printers. Each unit of regular requires 5 units of time in this machine, and each unit of high-speed requires 3 units of time. The total time available in this machine per month is 10,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. The appropriate constraint/s will be
A)
B)
C)
D) A and C
E) B and C
14. XYZ Inc. produces two types of printers—regular and high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. XYZ is committed to using at least 5,000 units of recycled plastic per month. A critical machine is needed to manufacture the printers. Each unit of regular requires 5 units of time in this machine, and each unit of high-speed requires 3 units of time. The total time available in this machine per month is 15,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. The appropriate constraint/s will be
A)
B)
C)
D) A and C
E) B and C
15. XYZ Inc. produces two types of printers, called regular and high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. XYZ is committed to using at least 5,000 units of recycled plastic per month. A critical machine is needed to manufacture the printers. Each unit of regular requires 5 units of time in this machine, and each unit of high-speed requires 3 units of time. The total time available in this machine per month is 10,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. Imposing both of these constraints and non-negativity constraints, one of the feasible corner points is (assuming the first number in parenthesis is and the second number in parenthesis is )
A) (0,0)
B) (2000,0)
C) none exists
D) (0,5000)
E) (2500,0)
16. XYZ Inc. produces two types of printers—regular and high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. XYZ is committed to using at least 5,000 units of recycled plastic per month. A critical machine is needed to manufacture the printers. Each unit of regular requires 5 units of time in this machine, and each unit of high-speed requires 3 units of time. The total time available in this machine per month is 15,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. Imposing both of these constraints and non-negativity constraints, one of the feasible corner points is (assuming the first number in parenthesis is and the second number in parenthesis is )
A) (0,0)
B) (2000,0)
C) none exists
D) (0,5000)
E) (1500,0)
17. XYZ Inc. produces two types of printers—regular and high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. XYZ is committed to using at least 5,000 units of recycled plastic per month. A critical machine is needed to manufacture the printers. Each unit of regular requires 10 units of time in this machine, and each unit of high-speed requires 3 units of time. The total time available in this machine per month is 15,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. Imposing both of these constraints and non-negativity constraints, one of the feasible corner points is (assuming the first number in parenthesis is and the second number in parenthesis is )
A) (0,0)
B) (2500,0)
C) none exists
D) (0,5000)
E) (1500,0)
18. XYZ Inc. produces two types of printers—regular and high-speed. Net contribution is $50.00 per unit from regular and $70.00 per unit from high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. XYZ is committed to using at least 5,000 units of recycled plastic per month. A critical machine is needed to manufacture the printers. Each unit of regular requires 10 units of time in this machine and each unit of high-speed requires 3 units of time in this machine. The total time available in this machine per month is 15,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. Imposing both of these constraints and non-negativity constraints, the optimal solution to this problem (assuming the first number in parenthesis is and the second number in parenthesis is ) will be
A) (0,0)
B) (2500,0)
C) none exists
D) (0,5000)
E) (1500,0)
19. XYZ Inc. produces two types of printers—regular and high-speed. Net contribution is $50.00 per unit from regular and $70.00 per unit from high-speed. Regular uses 2 units of recycled plastic per unit, and high-speed uses 1 unit of recycled plastic per unit of production. XYZ is committed to using at least 5,000 units of recycled plastic per month. A critical machine is needed to manufacture the printers. Each unit of regular requires 10 units of time in this machine and each unit of high-speed requires 3 units of time in this machine. The total time available in this machine per month is 15,000 units. Let be the number of units of regular produced per month and the number of units of high-speed produced per month. Imposing both of these constraints and non-negativity constraints, the objective function value corresponding to the optimal solution to this problem (assuming the first number in parenthesis is and the second number in parenthesis is ) will be
A) 350000
B) 125000
C) none exists
D) 250000
E) 35000
20. Constraint A: Constraint B:
The feasible region with these two constraints and non-negativity constraints
A) is closed
B) open and hence does not have an optimal solution
C) open but has an optimal solution
D) non-existent (any objective with this as the constraint region will be infeasible)
E) is closed and will have an optimal solution for any linear objective function
Multiple Choice Questions for Chapter 8 (Linear Programming Applications)
1. In using the Solver package to solve a linear programming problem, the decision variables are assigned to the
A) target cell (or cells)
B) changing cell (or cells)
C) constraint cells
D) variable cells
2. In using the Solver package to solve a linear programming problem, the objective function expression and its value are defined in the
A) target cell (or cells)
B) changing (or cells)
C) constraint cells
D) variable cells
3. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying the objective function of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions
4. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying the objective function of Problem A by a negative constant and leaving all other things unchanged. Problems A and B may have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions.
5. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying constraint 1 of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions
6. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying all constraints of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions
7. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by adding a constant to the objective function of Problem A and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions
8. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by multiplying constraint 1 of Problem A by a negative constant and leaving all other things unchanged. Problems A and B may have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions
9. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained by adding a constant to the right hand side of Constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in the solutions
10. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by omitting the non-negativity constraints and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions
11. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by omitting constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions
12. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by dropping exactly one variable and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions
13. Problem A is a given formulation of a linear program with an optimal solution and exactly one equality constraint. Problem B is a formulation obtained from Problem A by replacing the equality constraint with a pair of inequality constraints obtained by serially replacing the equality sign of the constraint with ? and ? signs, leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions
14. Problem A is a given formulation of a linear program with an optimal solution, and its constraint 1 is ? type. Problem B is a formulation obtained from Problem A by replacing the ? constraint with an equality constraint and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions
15. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a redundant constraint, leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraints in the solutions
16. Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a constraint, and leaving all other things unchanged. Problems A and B will have
A) the same optimal solution and same objective function value
B) the same optimal solution but different objective function values
C) different optimal solutions but same objective function value
D) different optimal solutions and different objective function values
E) same or different solution profile depending on the role of the constraint in Problem B
17. In formulating a coffee blending problem where there are three types of coffee beans, the objective is to find a recipe to make 1 pound of blended coffee that satisfies a set of properties at the least cost. The decision variables are , , and , representing pounds (actually fractional pounds) of coffee beans used per pound of blended coffee. One of the constraints of the problem will be
A)
B)
C)
D) no such constraint is required
18. In formulating a coffee blending problem where there are three types of coffee beans, the objective is to find a recipe to make 1 pound of blended coffee that satisfies a set of properties at the least cost. The decision variables are , , and , representing pounds (actually fractional pounds) of coffee beans used per pound of blended coffee. Suppose that bitterness is a property measured as an index from 1 to 6 and a blend’s bitterness is given by the weighted average (using the weight fraction of each beans in the blend as the weight) of the bitterness of individual beans going into the blend. Suppose that the bitterness indices for the three beans are respectively 2, 4, and 5. A blend with bitterness in the range 3 to 4.5 is most desirable. The appropriate constraint/s will be
A)
B)
C) and
D) the constraint/s are not correct since weights are not correctly represented
19. In formulating a coffee blending problem where there are three types of coffee beans, the objective is to find a recipe to make 1 pound of blended coffee that satisfies a set of properties at the least cost. The decision variables are , , and, , representing pounds (actually fractional pounds) of coffee beans used per pound of blended coffee. Suppose that it is required to produce 200 pounds of coffee using this formulation. The appropriate constraint/s, given the definition of the problem and decision variables, will be
A)
B)
C)
D) and multiply the answer by 200 to blend 200 pounds
You will also have to deal with simple problems with quick calculations (Based on essay type. I will provide several Choices but you must verify and choose.) Here are few examples which may also appear in Part 2 of the Exam.
20. Wilkinson Auto Dealership sells standard automobiles and station wagons. The profit contribution for automobiles is $250.00 per unit and that for station wagons is $500.00 per unit. The company is planning the placement of orders with the manufacturer for next quarter. Orders for automobiles and station wagons can not exceed 320 and 160 respectively. Dealer preparation takes 2 hrs/auto and 5.00 hrs/wagon. They have 1100 hrs of preparation time next quarter. Autos take 1 unit of space, whereas wagons take 1.2 units of space. 480 units of space are available. In order to maintain some balance, the number of cars ordered should not be more than 150% the number of wagons ordered. Assume they can sell all the autos and wagons they order for the quarter. How many automobiles and wagons should be ordered in order to maximize total profit contribution? Define the decision variables, constraints, and the objective function for this problem.
Ans: Decision variables: Let be the number of automobiles and be the number of station wagons ordered next quarter
Objective function: Max:
Constraints:
Variables are non-negative
Optimal solution using Solver:
The objective function value corresponding to the optimal solution is $120,312.50
Multiple Choice Questions – LP General Definitions, Excel Applications & Sensitivity Analysis (questions applicable to Chapters 7 & 8 seen below) – Everything here is a must study for the exam; many of these questions are guaranteed to be on the exam.
1. Enlightened future managers should know which of the following?
a. The power and relevance of management science.
b. When management science can and cannot be applied.
c. How to apply the major techniques of management science.
d. How to interpret the results of a management science study.
e. All of these.
2. The rapid development of the management science discipline can be credited in part to:
a. World War I.
b. George Dantzig.
c. the computer revolution.
d. b. and c. only.
e. a., b., and c.
3. Managers may base their decisions on which of the following?
a. Quantitative factors.
b. Their best judgement.
c. Opinions from other managers.
d. Past experience.
e. All of these.
4. Management science is based strongly on which of the following fields?
a. Mathematics.
b. Computer science.
c. Business administration.
d. a. and b. only.
e. All of these.
5. Which of the following are components of a mathematical model for decision making?
a. Decision variables.
b. An objective function.
c. Constraints.
d. Parameters.
e. All of these.
6. Which of the following is a constant in a mathematical model?
a. Decision variable.
b. Parameter.
c. Objective function.
d. Constraint.
e. None of these.
7. Which of the following is an inequality or equation that expresses a restriction in a mathematical model?
a. Decision variable.
b. Parameter.
c. Objective function.
d. Constraint.
e. None of these.
8. Which of the following is an inequality or equation that expresses a restriction in a mathematical model?
a. Decision variable.
b. Parameter.
c. Objective function.
d. Constraint.
e. None of these.
9. A manager should know the following things about linear programming.
a. What it is.
b. When it should be used.
c. When it should not be used.
d. How to interpret the results of a study.
e. All of these.
10. Which of the following is not a component of a linear programming model?
a. Constraints.
b. Decision variables.
c. Parameters.
d. An objective.
e. A spreadsheet.
11. In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as:
a. optimal.
b. feasible.
c. nonnegative.
d. targeted.
e. All of these.
12. Which of the following functions is not linear?
A) 5X + 3Z
B) 3X + 4Y + Z – 3
C) 2X + 5YZ
D) Z
E) 2X – 5Y + 2Z
13. Which of the following is not one of the steps in formulating a linear program?
A) Graph the constraints to determine the feasible region.
B) Define the decision variables.
C) Use the decision variables to write mathematical expressions for the objective function and the constraints.
D) Identify the objective and the constraints.
E) Completely understand the managerial problem being faced.
14. Which of the following is not acceptable as a constraint in a linear programming problem (minimization)?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5
15. What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?
A) resource mix
B) resource restriction
C) product restriction
D) resource allocation
E) product mix
Consider the sensitivity report below for the problems 16 to 20, which follow.
16. The optimal solution to this linear program is
A) x1 = 0, x2 = 0.
B) x1 = 34, x2 = 40.
C) x1 = 6, x2 = 11.
D) x1 = 7.33, x2 = 6.
E) x1 = 3, x2 = 6.
17. Which of the following constraints are binding?
A) Extrusion only
B) Packing only
C) Additive only
D) Extrusion and Packaging
E) All constraints are binding
18. What is the increase in the objective value if 2 units of extrusion are added?
A) 3
B) 6
C) 48
D) 96
E) Not enough information provided
19. What is the increase in the objective value if 2 units of packaging are added?
A) 11
B) 18
C) 22
D) 36
E) Not enough information provided
20. What is the increase in the objective value if 2 units of additive is added?
A) 0
B) 4
C) 12
D) 16
E) Not enough information provided
21. Consider the following linear programming problem:
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above
22. Which of the following could not be a constraint for a linear programming problem?
a. 1A + 2B ? 3.
b. 1A + 2B ? 3.
c. 1A + 2B = 3.
d. 1A + 2B.
e. 1A + 2B + 3C ? 3.
23. For the products A, B, C, and D, which of the following could be a linear programming objective function?
a. P = 1A + 2B +3C + 4D.
b. P = 1A + 2BC +3D.
c. P = 1A + 2AB +3ABC + 4ABCD.
d. P = 1A + 2B/C +3D.
e. All of these.
24. After the data is collected the next step to formulating a linear programming model is to:
a. identify the decision variables.
b. identify the objective function.
c. identify the constraints.
d. specify the parameters of the problem.
e. None of these.
25. When using the graphical method, the region that satisfies all of the constraints of a linear programming problem is called the:
a. optimum solution space.
b. region of optimality.
c. profit maximization space.
d. feasible region.
e. region of non-negativity.
26. Solving linear programming problems graphically,
a. is possible with any number of decision variables.
b. provides geometric intuition about what linear programming is trying to achieve.
c. will always result in an optimal solution.
d. All of these.
e. None of these.
Multiple Choice Questions for Chapter 9 (Transportation, Transshipment & Assignment Problems)
1. In a transportation problem with 5 supply points, 3 demand points, and total supply equaling total demand, the number of decision variables will be
A) 5
B) 8
C) 15
D) 125
2. In a transportation problem with 5 supply points, 3 demand points, and total supply greater than total demand, the number of decision variables will be
A) 5
B) 9
C) 15
D) 20
3. In a transportation problem with 5 supply points, 3 demand points, and total supply less than total demand, the number of decision variables will be
A) 6
B) 9
C) 15
D) 18
4. If one formulates a transportation problem with 5 supply points, 3 demand points, and total supply greater than total demand, as a linear programming problem, the number of constraints will be
A) 5
B) 8
C) 3
D) 15
5. Using transportation problem formulation to help a location decision where there are two potential locations to choose from, one has to solve _____ transportation problems.
A) 3
B) 2
C) 1
D) several
6. In the transportation problem model for production planning discussed in your text, if there are 3 periods and 4 methods of manufacturing in each period, how many rows will be needed?
A) 12
B) 7
C) 13
D) 8
7. In the transportation problem model for production planning discussed in your text, if there are 3 periods and 4 methods of manufacturing in each period, how many columns will be needed?
A) 3
B) 4
C) 5
D) 8
8. In the linear programming formulation of the transportation problem, cost of transporting one unit of the material from a supply point to a demand point appears in
A) the objective function only
B) the constraints only
C) both objective function and
