Quantitative Analysis for Management, 11e (Render)
Chapter 8 Linear Programming Applications
1) In a production scheduling problem, the inventory at the end of this month is set equal to the inventory at the
end of last month + last month’s production − sales this month.
2) Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a
product.
3) Determining the mixture of ingredients for a most economical feed or diet combination would be described as
a production mix type of linear program.
4) A media selection LP application describes a method in which media producers select customers.
5) The constraints in a transportation problem deal with requirements at each origin and capacities at each
destination.
6) An ingredient or blending problem is a special case of the more general problem known as diet and feed mix
problems.
7) In general, linear programming is unable to solve complex labor planning as the objective function is usually
not definable.
8) Linear programming variable names such as X11, X12, X13, could possibly be used to represent production of a
product (X1j ) over several months.
9) Since the production mix linear program applications are a special situation, the number of decision variables
is limited to two.
10) In formulating the media selection linear programming model, we are unable to take into account the
effectiveness of a particular presentation (e.g., the fact that only 5 percent of the people exposed to a radio ad will
respond as desired).
11) A marketing research linear programming model can help a researcher structure the least expensive,
statistically meaningful sample.
12) Another name for the transportation problem is the logistics problem.
13) Transporting goods from several origins to several destinations efficiently is called the transportation
problem.
14) The linear programming approach to media selection problems is typically to either maximize the number of
ads placed per week or to minimize advertising costs.
15) The linear programming model of the production mix problem only includes constraints of the less than or
equal form.
16) The linear programming model of the production scheduling process can include the impact of hiring and
layoffs, regular and overtime pay rates, and the desire to have a constant and stable production schedule over a
several–month period.
17) The linear programming model of the production scheduling process is usually used when we have to
schedule the production of a single product, requiring a mix of resources, over time.
18) The linear programming model of the production scheduling process is usually used when we have to
schedule the production of multiple products, each of which requires a set of resources not required by the other
products, over time.
19) Production scheduling is amenable to solution by LP because it is a problem that must be solved on a regular
basis.
20) If a linear programming problem has alternate solutions, the order in which you enter the constraints may
affect the particular solution found.
21) In the linear programming transportation model, the coefficients of the objective function can represent either
the cost or the profit from shipping goods along a particular route.
22) The linear programming transportation model allows us to solve problems where supply does not equal
demand.
23) The linear programming truck loading model always results in a practical solution.
24) The linear programming ingredient or blending problem model allows one to include not only the cost of the
resource, but also the differences in composition.
25) Using linear programming to maximize audience exposure in an advertising campaign is an example of the
type of linear programming application known as
A) media selection.
B) marketing research.
C) portfolio assessment.
D) media budgeting.
E) All of the above
26) The selection of specific media from among a wide variety of alternatives is the type of LP problem known as
A) the product mix problem.
B) the investment banker problem.
C) the Wall Street problem.
D) the portfolio selection problem.
E) None of the above
27) The following does not represent a factor a manager might typically consider when employing linear
programming for a production scheduling:
A) labor capacity.
B) space limitations.
C) product demand.
D) risk assessment.
E) inventory costs.
Table 8–1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the
manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of
finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of
inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours
of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is
to be used to develop a production schedule. Define the variables as follows:
28) According to Table 8–1, which describes a production problem, what would the objective function be?
A) Maximize T + C
B) Maximize 120T + 80C
C) Maximize 200T + 200 C
D) Minimize 6T + 5C
E) None of the above
29) According to Table 8–1, which describes a production problem, which of the following would be a necessary
constraint in the problem?
A) T + C ≤ 40
B) T + C ≤ 200
C) T + C ≤ 180
D) 120T + 80C ≥ 1000
E) None of the above
30) According to Table 8–1, which describes a production problem, which of the following would be a necessary
constraint in the problem?
A) T + C ≥ 40
B) 3T + 2C ≤ 200
C) 2T + 2C ≤ 40
D) 120T + 80C ≥ 1000
E) None of the above
31) According to Table 8–1, which describes a production problem, suppose it is decided that there must be 4
chairs produced for every table. How would this constraint be written?
A) T ≥ C
B) T ≤ C
C) 4T = C
D) T = 4C
32) According to Table 8–1, which describes a production problem, suppose it is decided that the number of hours
used in the assembly process must be at least 80 percent of the time available. How would this constraint be
written?
A) 3T + 2C ≥ 160
B) 3T + 2C ≥ 200
C) 3T + 2C ≤ 200
D) 3T + 2C ≤ 160
E) None of the above
33) According to Table 8–1, which describes a production problem, suppose it is decided that the number of hours
used in the assembly process must be at least 90 percent of the number of hours used in the finishing department.
How would this constraint be written?
A) 3T + 2C ≥ 162
B) 3T + 2C ≥ 0.9(2T + 2C)
C) 3T + 2C ≤ 162
D) 3T + 2C ≤ 0.9(2T + 2C)
E) None of the above
34) Media selection problems are typically approached with LP by either
A) maximizing audience exposure or maximizing number of ads per time period.
B) maximizing the number of different media or minimizing advertising costs.
C) minimizing the number of different media or minimizing advertising costs.
D) maximizing audience exposure or minimizing advertising costs.
E) minimizing audience exposure or minimizing advertising costs.
35) Which of the following is considered a decision variable in the media selection problem of maximizing
audience exposure?
A) the amount spent on each ad type
B) what types of ads to offer
C) the number of ads of each type
D) the overall advertising budget
E) None of the above
36) Which of the following is considered a decision variable in the media selection problem of minimizing
interview costs in surveying?
A) the number of people to survey in each market segment
B) the overall survey budget
C) the total number surveyed
D) the number of people to conduct interviews
E) None of the above
37) In production scheduling LP problems, inventory at the end of this month is set equal to ________.
A) inventory at the end of last month + this month’s production − this month’s sales
B) inventory at the beginning of last month + this month’s production − this month’s sales
C) inventory at the end of last month + last month’s production − this month’s sales
D) inventory at the beginning of last month + last month’s production − last month’s sales
E) inventory at the end of last month – this month’s production + this month’s sales
38) Which of the following is considered a decision variable in the production mix problem of maximizing profit?
A) the amount of raw material to purchase for production
B) the number of product types to offer
C) the selling price of each product
D) the amount of each product to produce
E) None of the above
Table 8–2
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the
manufacturing process: assembly, finishing, and inspection. Each table requires 4 hours of assembly, 3 hours of
finishing, and 1 hour of inspection. Each chair requires 3 hours of assembly, 2 hours of finishing, and 2 hours of
inspection. The selling price per table is $140 while the selling price per chair is $90. Currently, each week there
are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time. Assume
that one hour of assembly time costs $5.00; one hour of finishing time costs $6.00; one hour of inspection time
costs $4.50; and that whatever labor hours are not required for the table and chairs can be applied to another
product. Linear programming is to be used to develop a production schedule. Define the variables as follows:
39) According to Table 8–2, which describes a production problem, what would the objective function be?
A) Maximize T + C
B) Maximize 140T + 90C
C) Minimize 42.5T + 36C
D) Maximize 97.5T + 54C
E) Maximize 124.5T + 74.5C
40) According to Table 8–2, which describes a production problem, suppose it was decided that all the labor hour
costs have to be covered through the sale of the tables and chairs, regardless of whether or not all the labor hours
are actually used. How would the objective function be written?
A) Maximize 140T + 90C
B) Minimize 140T + 90C
C) Maximize 97.5T + 54C
D) Maximize T + C
E) Maximize 140T + 90C – 1100(T+C) – 960(T+C) – 202.5(T+C)
41) According to Table 8–2, which describes a production problem, suppose you realize that you can trade off
assembly hours for finishing hours, but that the total number of finishing hours, including the trade–off hours,
cannot exceed 240 hours. How would this constraint be written?
A) 7T + 5C ≤ 360
B) 3T + 2C ≤ 240
C) 4T + 3C ≤ 140
D) −T − C ≤ 80
E) None of the above
42) Suppose that the problem described in Table 8–2 is modified to specify that one–third of the tables produced
must have 6 chairs, one–third must have 4 chairs, and one–third must have 2 chairs. How would this constraint be
written?
A) C = 4T
B) C = 2T
C) C = 3T
D) C = 6T
E) None of the above
Table 8–3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12
profit. Kent’s firm is small and its resources limited. During any given production period (of 1 week), 10 gallons
of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1
gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
43) Referring to Table 8–3, if we were to frame this as a linear programming problem, the objective function would
be:
A) Maximize 9B + 12T.
B) Maximize 9T + 12B.
C) Minimize 10T + 10B.
D) Maximize 12T + 10B.
E) None of the above
44) Referring to Table 8–3, which of the following constraints would be used?
A) 10T + 12B ≤ 12
B) 1T + 1B ≤ 10
C) 1T + 2B ≥ 12
D) All of the above
E) None of the above
45) Referring to Table 8–3, which of the following constraints would be used?
A) Maximize 9T + 12B
B) 9T + 12B ≥ 12
C) 12T + 9B ≤ 10
D) 10T + 10B ≥ 10
E) None of the above
46) Referring to Table 8–3, suppose that this problem requires that you use all the varnish for the week. How
would the linear programming representation change?
A) 1B + 1T ≤ 10 will become 1B + 1T ≤ 12.
B) 1B + 1T ≤ 10 will be replaced by 1B + 1T ≥ 10.
C) 1B + 1T ≤ 10 will become 1B + 1T = 10.
D) 2B + 1T ≤ 12 will become 2B + 1T = 12.
E) None of the above
47) Referring to Table 8–3, the solution to the problem is
A) T = 10, B = 0.
B) T = 0, B = 10.
C) T = 0, B = 6.
D) T = 8, B = 2.
E) None of the above
48) Referring to Table 8–3, which of the following constraints would be used?
A) 9T + 12B ≤ 12
B) 1T + 1B ≥ 10
C) 1T + 2B ≤ 12
D) All of the above
E) None of the above
Table 8–4
The following is a linear programming formulation of a labor planning problem. There are four overlapping
shifts, and management must decide how many employees to schedule to start work on each shift. The objective
is to minimize the total number of employees required while the constraints stipulate how many employees are
required at each time of day. The variables X1 – X4 represent the number of employees starting work on each
shift (shift 1 through shift 4).
49) According to Table 8–4, which describes a labor planning problem and its solution, how many workers would
be assigned to shift 1?
A) 12
B) 13
C) 0
D) 2
E) None of the above
50) According to Table 8–4, which describes a labor planning problem and its solution, how many workers would
be assigned to shift 3?
A) 13
B) 14
C) 16
D) 0
E) None of the above
51) According to Table 8–4, which describes a labor planning problem and its solution, how many workers would
be assigned to shift 2?
A) 2
B) 0
C) 14
D) 15
E) None of the above
52) According to Exhibit 8–4, which describes a labor planning problem and its solution, how many workers
would be assigned to shift 4?
A) 1
B) 0
C) 14
D) 16
E) None of the above
53) According to Table 8–4, which describes a labor planning problem and its solution, how many workers would
actually be on duty during shift 1?
A) 12
B) 13
C) 0
D) 29
E) None of the above
54) Linear programming is usually used by managers involved in portfolio selection to
A) maximize return on investment.
B) maximize investment limitations.
C) maximize risk.
D) minimize risk.
E) minimize expected return on investment.
55) The selection of specific investments from among a wide variety of alternatives is the type of LP problem
known as
A) the product mix problem.
B) the investment banker problem.
C) the Wall Street problem.
D) the portfolio selection problem.
E) None of the above
56) What is another name for blending problems?
A) diet problems
B) ingredient problems
C) feed mix problems
D) production mix problems
E) media selection problems
Table 8–5
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she
also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible
ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money
market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be
invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money
invested in all three alternatives. In formulating this as a linear programming problem, define the variables as
follows:
57) According to Table 8–5, which describes an investment problem, which of the following would be the most
appropriate constraint in the linear programming problem?
A) 0.06C + 0.13S + 0.08M ≤ 200000
B) C + S + M ≥ 200000
C) C + S + M ≤ 200000
D) C + S + M = 200000
E) None of the above
58) According to Table 8–5, which describes an investment problem, suppose that Ivana has decided that the
amount invested in stocks cannot exceed one–fourth of the total amount invested. Which is the best way to write
this constraint?
A) S ≤ 100,000/4
B) 0.13S ≤ 0.24C + 0.32M
C) –C + 4S – M ≤ 0
D) S ≤ (C + M) / 4
E) –C + 3S – M ≤ 0
59) According to Table 8–5, which describes an investment problem, suppose that Ivana has assigned the
following risk factors to each investment instrument CDs (C): 1.2; stocks (S): 4.8; money market mutual fund
(M): 3.2. If Ivana decides that she wants the risk factor for the whole investment to be less than 3.3, how should
the necessary constraint be written?
A) 1.2C + 4.8S + 3.2M ≤ 3.3
B) C + S + M ≤ 3.3
C) 1.2C + 4.8S + 3.2M ≤ 3.3(C + S + M)
D) (1.2C + 4.8S + 3.2M)/3 ≤ 3.3
E) S = 0
60) When formulating transportation LP problems, constraints usually deal with the
A) number of items to be transported.
B) shipping cost associated with transporting goods.
C) distance goods are to be transported.
D) number of origins and destinations.
E) capacities of origins and requirements of destinations.
61) The following problem type is such a special case of linear programming that a special algorithm has been
developed to solve it:
A) the production mix problem.
B) the diet problem.
C) the ingredient mix problem.
D) the transportation problem.
E) None of the above
62) When formulating transportation LP problems, the objective function usually deals with the
A) number of items to be transported.
B) choice of transportation mode (e.g., truck, airplane, railroad, etc.).
C) shipping cost or distances associated with transporting goods.
D) number of origins and destinations.
E) capacities of origins and requirements of destinations.
63) The shipping problem in LP is also called the
A) production mix problem.
B) freight train problem.
C) transportation problem.
D) land and sea problem.
E) None of the above
64) When applying linear programming to diet problems, the objective function is usually designed to
A) maximize profits from blends of nutrients.
B) maximize ingredient blends.
C) minimize production losses.
D) maximize the number of products to be produced.
E) minimize the costs of nutrient blends.
65) Which of the following statements is true regarding the labor planning problem?
A) It is typically a maximization problem.
B) Required labor hours translate into less–than–or–equal–to constraints.
C) The decision variables can include how many full and part–time workers to use.
D) The problem is only unique to banks.
E) None of the above
66) Which of the following statements is false regarding the portfolio selection problem?
A) The typical objective is to maximize the expected return on investment
B) The contraints only pertain to risk
C) Typical applications include banks, mutual funds, investment services, and insurance companies
D) The problem typically includes both greater–than–or–equal–to and less–than–or–equal–to constraints
E) The problem can also factor in legal requirements
67) What is the objective in the truck loading problem?
A) minimize trucking distance
B) minimize the weight of the load shipped
C) maximize the value of the load shipped
D) minimize the cost of the load shipped
E) None of the above
68) What is the objective in the diet problem?
A) maximize nutrition
B) minimize number of ingredients
C) minimize calories
D) minimize cost
E) None of the above
69) What are the decision variables in the diet problem?
A) amount of each ingredient to use
B) number of ingredients to use
C) amount of each type of food to purchase
D) number of items of food to purchase
E) None of the above