Chapter 1—Introduction

MULTIPLE CHOICE

	1.	The field of management science
a.	concentrates on the use of quantitative methods to assist in decision making.	
b.	approaches decision making rationally, with techniques based on the scientific method.	
c.	is another name for decision science and for operations research.	
d.	each of these choices are true.	

ANS:	D	PTS:	1	TOP:	Introduction

	2.	Identification and definition of a problem
a.	cannot be done until alternatives are proposed.	
b.	is the first step of decision making.	
c.	is the final step of problem solving.	
d.	requires consideration of multiple criteria.	

ANS:	B	PTS:	1	TOP:	Problem solving and decision making

	3.	Decision alternatives
a.	should be identified before decision criteria are established.	
b.	are limited to quantitative solutions	
c.	are evaluated as a part of the problem definition stage.	
d.	are best generated by brain-storming.	

ANS:	A	PTS:	1	TOP:	Problem solving and decision making

	4.	Decision criteria
a.	are the choices faced by the decision maker.	
b.	are the problems faced by the decision maker.	
c.	are the ways to evaluate the choices faced by the decision maker.	
d.	must be unique for a problem.	

ANS:	C	PTS:	1	TOP:	Problem solving and decision making

	5.	In a multicriteria decision problem
a.	it is impossible to select a single decision alternative.	
b.	the decision maker must evaluate each alternative with respect to each criterion.	
c.	successive decisions must be made over time.	
d.	each of these choices are true.	

ANS:	B	PTS:	1	TOP:	Problem solving and decision making

	6.	The quantitative analysis approach requires
a.	the manager's prior experience with a similar problem.	
b.	a relatively uncomplicated problem.	
c.	mathematical expressions for the relationships.	

ANS:	C	PTS:	1	TOP:	Quantitative analysis and decision making

	7.	A physical model that does not have the same physical appearance as the object being modeled is
a.	an analog model.	
b.	an iconic model.	
c.	a mathematical model.	
d.	a qualitative model.	

ANS:	A	PTS:	1	TOP:	Model development	

	8.	Inputs to a quantitative model
a.	are a trivial part of the problem solving process.	
b.	are uncertain for a stochastic model.	
c.	are uncontrollable for the decision variables.	
d.	must all be deterministic if the problem is to have a solution.	

ANS:	B	PTS:	1	TOP:	Model development	

	9.	When the value of the output cannot be determined even if the value of the controllable input is known, the model is
a.	analog.	
b.	digital.	
c.	stochastic.	
d.	deterministic.	

ANS:	C	PTS:	1	TOP:	Model development	

	10.	The volume that results in total revenue being equal to total cost is the
a.	break-even point.	
b.	marginal volume.	
c.	marginal cost.	
d.	profit mix.	

ANS:	A	PTS:	1	TOP:	Break-even analysis	

	11.	Management science and operations research both involve
a.	qualitative managerial skills.	
b.	quantitative approaches to decision making.	
c.	operational management skills.	
d.	scientific research as opposed to applications.	

ANS:	B	PTS:	1	TOP:	Introduction

	12.	George Dantzig is important in the history of management science because he developed
a.	the scientific management revolution.	
b.	World War II operations research teams.	
c.	the simplex method for linear programming.	
d.	powerful digital computers.	

ANS:	C	PTS:	1	TOP:	Introduction

	13.	The first step in problem solving is
a.	determination of the correct analytical solution procedure.	
b.	definition of decision variables.	
c.	the identification of a difference between the actual and desired state of affairs.	
d.	implementation.	

ANS:	C	PTS:	1	TOP:	Problem solving and decision making

	14.	Problem definition
a.	includes specific objectives and operating constraints.	
b.	must occur prior to the quantitative analysis process.	
c.	must involve the analyst and the user of the results.	
d.	each of these choices are true.	

ANS:	D	PTS:	1	TOP:	Quantitative analysis	

	15.	A model that uses a system of symbols to represent a problem is called
a.	mathematical.	
b.	iconic.	
c.	analog.	
d.	constrained.	

ANS:	A	PTS:	1	TOP:	Model development	

	16.	Which of the following is not one of the commonly used names for the body of knowledge involving quantitative approaches to decision-making?
a.	management science	
b.	business analytics	
c.	operations research	
d.	efficiency studies	

ANS:	D	PTS:	1	TOP:	Introduction

TRUE/FALSE

	1.	The process of decision making is more limited than that of problem solving.

ANS:	T	PTS:	1	TOP:	Problem solving and decision making

	2.	The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis.

ANS:	F	PTS:	1	TOP:	Model development	

	3.	The volume that results in marginal revenue equaling marginal cost is called the break-even point.

ANS:	F	PTS:	1	TOP:	Problem solving and decision making

	4.	Problem solving encompasses both the identification of a problem and the action to resolve it.

ANS:	T	PTS:	1	TOP:	Problem solving and decision making

	5.	The decision making process includes implementation and evaluation of the decision.

ANS:	F	PTS:	1	TOP:	Problem solving and decision making

	6.	The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured.

ANS:	F	PTS:	1	TOP:	Quantitative analysis	

	7.	The value of any model is that it enables the user to make inferences about the real situation.

ANS:	T	PTS:	1	TOP:	Model development	

	8.	Uncontrollable inputs are the decision variables for a model.

ANS:	F	PTS:	1	TOP:	Model development	

	9.	The feasible solution is the best solution possible for a mathematical model.

ANS:	F	PTS:	1	TOP:	Model solution	

	10.	A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input.

ANS:	F	PTS:	1	TOP:	Model development	

	11.	Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940's.

ANS:	F	PTS:	1	TOP:	Introduction

	12.	To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.

ANS:	F	PTS:	1	TOP:	Problem solving and decision making

	13.	The most critical component in determining the success or failure of any quantitative approach to decision making is problem definition.

ANS:	T	PTS:	1	TOP:	Quantitative analysis	

	14.	The first step in the decision making process is to identify the problem.

ANS:	T	PTS:	1	TOP:	Introduction

	15.	All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.

ANS:	T	PTS:	1	TOP:	Quantitative analysis	

	16.	In quantitative analysis, the optimal solution is the mathematically-best solution.

ANS:	T	PTS:	1	TOP:	Quantitative analysis	

	17.	If you are deciding to buy either machine A, B, or C with the objective of minimizing the sum of labor, material and utility costs, you are dealing with a single-criterion decision.

ANS:	T	PTS:	1	TOP:	Problem solving and decision making

	18.	Model development should be left to quantitative analysts; the model user's involvement should begin at the implementation stage.

ANS:	F	PTS:	1	TOP:	Problem solving and decision making

	19.	A feasible solution is one that satisfies at least one of the constraints in the problem.

ANS:	F	PTS:	1	TOP:	Model solution	

	20.	A toy train layout designed to represent an actual railyard is an example of an analog model.

ANS:	F	PTS:	1	TOP:	Model development	

SHORT ANSWER

	1.	Should the problem solving process be applied to all problems?

ANS:	
Answer not provided.

PTS:	1	TOP:	Problem solving and decision making	

	2.	Explain the difference between quantitative and qualitative analysis from the manager's point of view.

ANS:	
Answer not provided.

PTS:	1	TOP:	Quantitative analysis and decision making	

	3.	Explain the relationship among model development, model accuracy, and the ability to obtain a solution from a model.

ANS:	
Answer not provided.

PTS:	1	TOP:	Model solution	

	4.	What are three of the management science techniques that practitioners use most frequently? How can the effectiveness of these applications be increased?

ANS:	
Answer not provided.

PTS:	1	TOP:	Methods used most frequently

	5.	What steps of the problem solving process are involved in decision making?

ANS:	
Answer not provided.

PTS:	1	TOP:	Quantitative analysis and decision making	

	6.	Give three benefits of model development and an example of each.

ANS:	
Answer not provided.

PTS:	1	TOP:	Model development	

	7.	Explain the relationship between information systems specialists and quantitative analysts in the solution of large mathematical problems.

ANS:	
Answer not provided.

PTS:	1	TOP:	Data preparation	

	8.	Discuss two developments that occurred during the post-World War II period that led to the growth and use of quantitative methods in nonmilitary applications.

ANS:	
Answer not provided.

PTS:	1	TOP:	Introduction

	9.	Discuss at least three characteristics of a problem that make it a good candidate for using a quantitative approach to analyze it.

ANS:	
Answer not provided.

PTS:	1	TOP:	Quantitative analysis and decision making	

PROBLEM

	1.	A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $5.50 and the price per unit of the Illinois corn is $6.00.
a.	Define variables that would tell how many units to purchase from each source.	
b.	Develop an objective function that would minimize the total cost.	
c.	The manufacturer needs at least 12000 units of corn. The Iowa cooperative can supply up to 8000 units, and the Illinois cooperative must supply at least 6000 units. Develop constraints for these conditions.	

ANS:	

a.	Let x1 = the number of units from Iowa	
	Let x2 = the number of units from Illinois	
b.	Min 5.5x1 + 6x2	
c.	x1 + x 2 ³ 12000	
	x1 < 8000	
	x1 ³ 6000	

PTS:	1	TOP:	Model development	

	2.	The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Here, price can vary between $10 and $50.
a.	How many units can be sold at the $10 price? How many can be sold at the $50 price?	
b.	Model the expression for total revenue.	
c.	Consider prices of $20, $30, and $40. Which price alternative will maximize total revenue? What are the values for demand and revenue at this price?	

ANS:	

a.	For p = 10, d = 4750	
	For p = 50, d = 3750	
b.	TR = p(5000 - 25p)	
c.	For p = 20, TR = $90,000	
	For p = 30, TR = $127,500	
	For p = 40, TR = $160,000	
	Best price is p = 40. Demand = 4000	

PTS:	1	TOP:	Model development	

	3.	There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45.
a.	Write an expression for total cost.	
b.	Write an expression for total revenue.	
c.	Write an expression for total profit.	
d.	Find the break-even point.	

ANS:	

a.	C(x) = 50000 + 25x	
b.	R(x) = 45x	
c.	P(x) = 45x - (50000 + 25x)	
d.	x = 2500	

PTS:	1	TOP:	Breakeven analysis	

	4.	An author has received an advance against royalties of $10,000. The royalty rate is $1.00 for every book sold in the United States, and $1.35 for every book sold outside the United States. Define variables for this problem and write an expression that could be used to calculate the number of books to be sold to cover the advance.

ANS:	
Let x1 = the number of books sold in the U.S.
Let x2 = the number of books sold outside the U.S.

10000 = 1x1 + 1.35x2

PTS:	1	TOP:	Breakeven analysis	

	5.	A university schedules summer school courses based on anticipated enrollment. The cost for faculty compensation, laboratories, student services, and allocated overhead for a computer class is $8500. If students pay $420 to enroll in the course, how large would enrollment have to be for the university to break even?

ANS:	
Enrollment would need to be 21 students.

PTS:	1	TOP:	Breakeven analysis	

	6.	As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:

Monthly fixed cost (loan payment, taxes, insurance, maintenance)	$6000	
Variable cost per occupied room per night	$    20	
Revenue per occupied room per night	$    75	

a.	Write the expression for total cost per month. Assume 30 days per month.	
b.	Write the expression for total revenue per month.	
c.	If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even?	

ANS:	

a.	C(x) = 6000 + 20(30)x     (monthly)	
b.	R(x) = 75(30)x     (monthly)	
c.	Break-even occupancy = 3.64 or 4 occupied rooms per night, so they have enough rooms to break even. This would be a 33% occupancy rate.	

PTS:	1	TOP:	Breakeven analysis	

	7.	Organizers of an Internet training session will charge participants $150 to attend. It costs $3000 to reserve the room, hire the instructor, bring in the equipment, and advertise. Assume it costs $25 per student for the organizers to provide the course materials.
a.	How many students would have to attend for the company to break even?	
b.	If the trainers think, realistically, that 20 people will attend, then what price should be charged per person for the organization to break even?	

ANS:	

a.	C(x) = 3000 + 25x	
	R(x) = 150x	
	Break-even students = 24	
b.	Cost = 3000 + 25(20)	
	Revenue = 20p	
	Break-even price = 175	

PTS:	1	TOP:	Breakeven analysis	

	8.	In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume. Give the cell formula for
a.	cell E12, break-even volume.	
b.	cell E16, total revenue.	
c.	cell E17, total cost.	
d.	cell E19, profit/loss.	

	A	B	C	D	E	
1				
2				
3				
4	Break-even calculation		
5				
6		Selling price per unit	10	
7				
8		Costs		
9		  Fix cost	8400	
10		  Variable cost per unit	4.5	
11				
12		Break-even volume		
13				
14		Sample calculation		
15		  Volume	2000	
16		  Total revenue		
17		  Total cost		
18				
19		  Profit loss		

ANS:	

a.	=E9/(E6-E10)	
b.	=E15*E6	
c.	=E9+E10*E15	
d.	=E16-E17	

PTS:	1	TOP:	Spreadsheets for management science	

	9.	A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a.	Write a mathematical model representing the store's constraints.	
b.	Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model each of the following objectives:	
	1.	Maximize the total pieces of furniture displayed.	
	2.	Maximize the total expected number of daily sales.	
	3.	Maximize the total expected daily profit.	

ANS:	

a.	50s + 30c £ 800	
	s ³ 5	
	c ³ 5	
b.	(1)  Max s + c	
	(2)  Max .03s + .05c	
	(3)  Max 6s + 5c	

PTS:	1	TOP:	Model development	

	10.	A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time. Work area #2 has 48 hours of available production time. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and $6 per window.
a.	Define decision variables that will tell how many units to build (doors and windows).	
b.	Develop an objective function that will maximize profits.	
c.	Develop production constraints for work area #1 and #2.	

ANS:	

a.	Let D = the number of doors to build	
	Let N = the number of windows to build	
b.	Profit = 8D + 6W	
c.	4D + 2W £ 60	
	2D + 4W £ 48	

PTS:	1	TOP:	Model development	

	11.	A small firm builds television antennas. The investment in plan and equipment is $200,000. The variable cost per television antenna is $500. The price of the television antenna is $1000. How many television antennas would be needed for the firm to break even?

ANS:	
400 television antennae

PTS:	1	TOP:	Breakeven analysis	

	12.	As computer service center has the capacity to do 400 jobs per day. The expected level of jobs demanded per day is 250 per day. The fixed cost of renting the computer process is $200 per day. Space rents for $100 per day. The cost of material is $15 per unit of work and $.35 cents of labor per unit. What is the break-even level of work?

ANS:	
200 service units

PTS:	1	TOP:	Breakeven analysis	

	13.	To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs are estimated as follows. Annual fixed costs to operate the school are $30,000. The annual cost per car is $3000. The cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is $350. Let x be the number of cars and y be the number of students.
a.	Write an expression for total cost.	
b.	Write an expression for total revenue.	
c.	Write an expression for total profit.	
d.	The school offers the course eight times each year. Each time the course is offered, there are two sessions. If they decide to operate five cars, and if four students can be assigned to each car, will they break even?	

ANS:	

a.	C(x) = 30000 + 14000x	
b.	R(y) = 350y	
c.	P(x,y) = 350y - (30000 + 14000x)	
d.	Each car/instructor can serve up to (4 students/session)(2 sessions/course)(8 courses/year) = 64 students annually. Five cars can serve 320 students. If the classes are filled, then profit for five cars is	
	     350(320) - (30000 + 14000(5)) = 12000	
	so the school can reach the break-even point.	

PTS:	1	TOP:	Breakeven analysis	

	14.	Zipco Printing operates a shop that has five printing machines. The machines differ in their capacities to perform various printing operations due to differences in the machines' designs and operator skill levels. At the start of the workday there are five printing jobs to schedule. The manager must decide what the job-machine assignments should be.
a.	How could a quantitative approach to decision making be used to solve this problem?	
b.	What would be the uncontrollable inputs for which data must be collected?	
c.	Define the decision variables, objective function, and constraints to appear in the mathematical model.	
d.	Is the model deterministic or stochastic?	
e.	Suggest some simplifying assumptions for this problem.	

ANS:	

a.	A quantitative approach to decision making can provide a systematic way for deciding the job-machine pairings so that total job processing time is minimized.	
b.	How long it takes to process each job on each machine, and any job-machine pairings that are unacceptable.	
c.	Decision variables: one for each job-machine pairing, taking on a value of 1 if the pairing is used and 0 otherwise.	
	Objective function: minimize total job processing time.	
	Constraints: each job is assigned to exactly one machine, and each machine be assigned no more than one job.	
d.	Stochastic: job processing times vary due to varying machine set-up times, variable operator performance, and more.	
e.	Assume that processing times are deterministic (known/fixed).	

PTS:	1	TOP:	Model development	

	15.	Consider a department store that must make weekly shipments of a certain product from two different warehouses to four different stores.
a.	How could a quantitative approach to decision making be used to solve this problem?	
b.	What would be the uncontrollable inputs for which data must be gathered?	
c.	What would be the decision variables of the mathematical model? the objective function? the constraints?	
d.	Is the model deterministic or stochastic?	
e.	Suggest assumptions that could be made to simplify the model.	

ANS:	

a.	A quantitative approach to decision making can provide a systematic way to determine a minimum shipping cost from the warehouses to the stores.	
b.	Fixed costs and variable shipping costs; the demand each week at each store; the supplies each week at each warehouse.	
c.	Decision variables--how much to ship from each warehouse to each store; objective function--minimize total shipping costs; constraints--meet the demand at the stores without exceeding the supplies at the warehouses.	
d.	Stochastic--weekly demands fluctuate as do weekly supplies; transportation costs could vary depending upon the amount shipped, other goods sent with a shipment, etc.	
e.	Make the model deterministic by assuming fixed shipping costs per item, demand is constant at each store each week, and weekly supplies in the warehouses are constant.	

PTS:	1	TOP:	Model development	

	16.	Three production processes - A, B, and C - have the following cost structure:

Process	Fixed Cost
per Year	Variable Cost
per Unit	
A	$120,000	$3.00	
B	    90,000	  4.00	
C	    80,000	  4.50	

a.   What is the most economical process for a volume of 8,000 units?
b.   How many units per year must be sold with each process to have annual profits of $50,000 if the selling price is $6.95 per unit?
c.   What is the break-even volume for each process?

ANS:	
a.   C(x) = FC + VC(x)
Process A:   C(x) = $120,000 + $3.00(8,000) = $144,000 per year
Process B:   C(x) = $  90,000 + $4.00(8,000) = $122,000 per year
Process C:   C(x) = $  80,000 + $4.50(8,000) = $116,000 per year

Process C has the lowest annual cost for a production volume of 8,000 units.

b.   Q = (profit + FC)/(price - VC)
Process A:   Q = ($50,000 + $120,000)/($6.95 - $3.00) = 43,038 units
Process B:   Q = ($50,000 + $  90,000)/($6.95 - $4.00) = 47,458 units
Process C:   Q = ($50,000 + $  80,000)/($6.95 - $4.50) = 53,062 units

Process A requires the lowest production volume for an annual profit of $50,000.

c.   At breakeven, profit (the pretax profits per period) is equal to zero. 
Q = FC/(price - VC)
Process A:   Q = $120,000/ ($6.95 - $3.00) = 30,380 units
Process B:   Q = $  90,000/ ($6.95 - $4.00) = 30,509 units
Process C:   Q = $  80,000/ ($6.95 - $4.50) = 32,654 units

Process A has the lowest break-even quantity, while Process B’s is almost as low.

PTS:	1	TOP:	Breakeven analysis	

	17.	Jane Persico, facility engineer at the El Paso plant of Computer Products Corporation (CPC), is studying a process selection decision at the plant. A new printer is to be manufactured and she must decide whether the printer will be auto-assembled or manually assembled. The decision is complicated by the fact that annual production volume is expected to increase by almost 50% over three years.  Jane has developed these estimates for two alternatives for the printer assembly process:

		Auto-
Assembly
Process	Manual
Assembly
Process	
Annual fixed cost		$690,000	$269,000	
Variable cost per product    		$29.56	$31.69	
Estimated annual production				
(in number of products):	Year 1	152,000	152,000	
	Year 2    	190,000	190,000	
	Year 3    	225,000	225,000	

a.   Which production process would be the least-cost alternative in Years 1, 2, and 3?
b.   How much would the variable cost per unit have to be in Year 2 for the auto-assembly process to justify the additional annual fixed cost for the auto-assembly process over the manual assembly process?

ANS:	
a.   C(x) = fixed cost + variable cost(x)
Year 1:
CA  =  690,000  +  29.56(152,000)  =  $5,183,120
CM  =  269,000  +  31.69(152,000)  =  $5,085,880   (least-cost alternative)
Year 2:
CA  =  690,000  +  29.56(190,000)  =  $6,306,400
CM  =  269,000  +  31.69(190,000)  =  $6,290,100   (least-cost alternative)
Year 3:
CA  =  690,000  +  29.56(225,000)  =  $7,341,000   (least-cost alternative)
CM  =  269,000  +  31.69(225,000)  =  $7,399,250

b.   CA = CM
FCA + vA(190,000) = FCM + vM(190,000)
690,000 + v(190,000) = 269,000 + 31.69(190,000)
vA = (269,000 + 6,021,100 - 690,000)/190,000
vA = $29.47   (roughly a 0.3% reduction)

PTS:	1	TOP:	Cost and volume models