Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-48 A manager in charge of new product development can hire engineers and market researchers.
The annual salary of an engineer is $40,000, while a market researcher receives $20,000. The
marginal contributions of engineers and market researchers are:
Engineers (E)
Market Researchers (R)
Worker
Additional
New Products
Worker
Additional
New Products
1st
50
1st
20
2nd
40
2nd
15
3rd
30
3rd
10
4th
20
4th
5
5th
10
5th
2
Based on the above information, if the manager currently hires four engineers and one market
researcher, what must be true?
a. She is making the correct decision because
E R
MP MP=
.
b. More new products would be developed if she hires more engineers and fewer market
researchers.
c. More new products would be developed if she hires fewer engineers and more market
researchers.
d. She is not making the correct decision because engineers are more productive than
market researchers at all levels of output.
EPP
.
3-49 A radio manufacturer is experiencing theft problems at its warehouse and has decided to hire
security guards to reduce the thefts. The firm wants to minimize the net cost of warehouse thefts.
Number of
Security Guards
0
1
2
3
4
5
Given the above info, if each security guard is paid $200 a week and the cost of a stolen radio is
$25, how many security guards should the firm hire?
a. 1
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
b. 2
c. 3
d. 4
e. 5
3-50 A radio manufacturer is experiencing theft problems at its warehouse and has decided to hire
security guards to reduce the thefts. The firm wants to minimize the net cost of warehouse thefts.
Number of
Security Guards
0
1
2
3
4
5
Given the above info, if the cost of a stolen radio is $25, what is the MOST the firm would be
willing to pay to hire the first security guard?
a. $200
b. $250
c. $500
d. $750
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-51 A radio manufacturer is experiencing theft problems at its warehouse and has decided to hire
security guards to reduce the thefts. The firm wants to minimize the net cost of warehouse thefts.
Number of
Security Guards
0
1
2
3
4
5
Given the above info, if each security guard is paid $200 a week and the cost of a stolen radio is
$50, how many security guards should the firm hire?
a. 1
b. 2
c. 3
d. 4
e. 5
3-52 A radio manufacturer is experiencing theft problems at its warehouse and has decided to hire
security guards to reduce the thefts. The firm wants to minimize the net cost of warehouse thefts.
Number of
Security Guards
0
1
2
3
4
5
Given the above info, in order to minimize the NET cost of theft, a firm should choose the level
of theft prevention at which
a. theft is eliminated.
b. the marginal benefit of theft equals the marginal cost of the theft.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
c. the total benefit of theft prevention equals the total cost of the theft prevention.
d. the marginal benefit of theft prevention equals the marginal cost of preventing theft.
e. the total cost of theft prevention equals the total cost of preventing theft.
3-53 The manager of the customer service department at a bank can hire employees with a high school
degree (HS) who earn $10,000 annually or employees with a bachelor’s degree (B) who earn
$20,000. The manager wants to maximize the number of customers served given a fixed payroll.
Number of Additional Customers Served
Worker
High School Degree
Bachelor’s Degree
1st
80
90
2nd
60
80
3rd
50
60
4th
40
40
5th
35
35
6th
30
25
Given the above info, if the manager has a payroll of $80,000, how should the budget be allocated
in order to maximize the number of customers served?
a. Hire two HS and three B.
b. Hire four HS and two B.
c. Hire one HS and two B.
d. Hire three HS and one B.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-54 The manager of the customer service department at a bank can hire employees with a high school
degree (HS) who earn $10,000 annually or employees with a bachelor’s degree (B) who earn
$20,000. The manager wants to maximize the number of customers served given a fixed payroll.
Number of Additional Customers Served
Worker
High School Degree
Bachelor’s Degree
1st
80
90
2nd
60
80
3rd
50
60
4th
40
40
5th
35
35
6th
30
25
Given the above info, if the manager currently has three HS and three B, what must be true?
a. More customers could be served if the manager hires fewer HS and more B.
b. More customers could be served if the manager hires more HS and fewer B.
c. The manager is making the correct decision because the marginal contributions are
proportionate.
d. The manager is not making the correct decision because bachelor’s degree holders are
more productive at all levels of customer served.
PP
.
3-55 The manager of the customer service department at a bank can hire employees with a high school
degree (HS) who earn $10,000 annually or employees with a bachelor’s degree (B) who earn
$20,000. The manager wants to maximize the number of customers served given a fixed payroll.
Number of Additional Customers Served
Worker
High School Degree
Bachelor’s Degree
1st
80
90
2nd
60
80
3rd
50
60
4th
40
40
5th
35
35
6th
30
25
Given the above info, if the manager’s payroll is $120,000, what should be done to maximize the
number of customers served?
a. Hire six HS and three B.
b. Hire five HS and five B.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
c. Hire four HS and four B.
d. Hire two HS and five B.
3-56 A government agency is having problems with personal telephone calls made during working
hours. Because each minute of a personal call costs the agency $0.50 in wasted wages, it has
decided to hire operators to monitor calls. The agency wants to hire the number of operators that
will minimize the total cost of personal calls.
Number of
operators
Minutes of personal
calls(per week)
0
3900
1
2300
2
1300
3
600
4
100
5
0
Based on the above information, if operators receive $300 a week, how many operators should
the agency hire?
a. 0
b. 1
c. 3
d. 5
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-57 A government agency is having problems with personal telephone calls made during working
hours. Because each minute of a personal call costs the agency $0.50 in wasted wages, it has
decided to hire operators to monitor calls. The agency wants to hire the number of operators that
will minimize the total cost of personal calls.
Number of
operators
Minutes of personal
calls(per week)
0
3900
1
2300
2
1300
3
600
4
100
5
0
Based on the above information, what is the most the agency would be willing to pay the fifth
operator?
a. $100
b. $200
c. $400
d. $500
e. none of the above
3-58 A government agency is having problems with personal telephone calls made during working
hours. Because each minute of a personal call costs the agency $0.50 in wasted wages, it has
decided to hire operators to monitor calls. The agency wants to hire the number of operators that
will minimize the total cost of personal calls.
Number of
operators
Minutes of personal
calls(per week)
0
3900
1
2300
2
1300
3
600
4
100
5
0
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
Based on the above information, if operators receive $400 a week, what is the lowest possible
total cost of personal calls?
a. $ 650
b. $ 800
c. $1450
d. $1500
3-59 The optimal level of any activity is that level for which
a. total benefit exceeds total cost by the greatest amount.
b. marginal benefit exceeds marginal cost by the greatest possible amount.
c. both a and b
d. none of the above
3-60 Dr. X, an assistant professor at a large state university, is trying to decide how to allocate the 50
hours a week she spends working among the various activities expected of an assistant professor.
The professor wants to maximize her raise next year and the table shows estimates of how time
spent in each activity will contribute to her raise:
Total Amount of Raise From:
Hours Per Week
Research
Teaching
University Service
14
$200
$400
$200
15
400
450
250
16
550
490
295
17
675
525
320
18
775
555
340
19
850
570
355
20
900
580
365
21
905
585
370
Given the above information, how should she allocate her time?
a. 20 hours research, 15 hours teaching, 15 hours service
b. 17 hours research, 17 hours teaching, 16 hours service
c. 18 hours research, 16 hours teaching, 16 hours service
d. 20 hours research, 16 hours teaching, 14 hours service
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
e. none of the above
3-61 Dr. X, an assistant professor at a large state university, is trying to decide how to allocate the 50
hours a week she spends working among the various activities expected of an assistant professor.
The professor wants to maximize her raise next year and the table shows estimates of how time
spent in each activity will contribute to her raise:
Total Amount of Raise From:
Hours Per Week
Research
Teaching
University Service
14
$200
$400
$200
15
400
450
250
16
550
490
295
17
675
525
320
18
775
555
340
19
850
570
355
20
900
580
365
21
905
585
370
Given the above information, what is Dr. X’s maximum possible raise if she works 50 hours?
a. $1495
b. $1600
c. $1845
d. $1860
3-62 Dr. X, an assistant professor at a large state university, is trying to decide how to allocate the 50
hours a week she spends working among the various activities expected of an assistant professor.
The professor wants to maximize her raise next year and the table shows estimates of how time
spent in each activity will contribute to her raise:
Total Amount of Raise From:
Hours Per Week
Research
Teaching
University Service
14
$200
$400
$200
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
15
400
450
250
16
550
490
295
17
675
525
320
18
775
555
340
19
850
570
355
20
900
580
365
21
905
585
370
Given the above information, if she decides that she will work 54 hours a week instead, how
should she allocate her time?
a. 18 hours research, 18 hours teaching, 18 hours service
b. 21 hours research, 19 hours teaching, 14 hours service
c. 20 hours research, 17 hours teaching, 17 hours service
3-63 A dentist’s office, which wants to serve the maximum number of patients given a fixed payroll,
currently has two dentists and four dental hygienists. Dentists earn $60,000 a year and hygienists
earn $15,000 a year. If the office is hiring the optimal combination of dentists and hygienists, and
the last dentist hired served 120 additional patients, how many patients will the last hygienist
hired add?
a. 30
b. 60
c. 120
d. 240
3-64 A publishing house is using 400 printers and 200 printing presses to produce books. The printers’
wage rate is $20 and the price of a printing press is $100. The last printer added 20 books to total
output, while the last press added 50 books to total output. In order to maximize the number of
books published with a budget of $28,000, the publishing house
a. should continue to use 400 printers and 200 presses.
b. should use more printers and fewer presses because printers cost less than presses.
c. should use more printers and fewer presses because the last dollar spent on a printer
yielded more output than the last dollar spent on a press.
d. should use more presses and fewer printers because the marginal output of the last press
was more than the marginal output of the last printer.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
e. should use more presses and fewer printers because the last dollar spent on a press
yielded more output than the last dollar spent on a printer.
3-65 A housecleaning company receives $25 for each house cleaned. The table below gives the
relation between the number of workers and the number of houses that can be cleaned per week.
Number of Workers
Houses Cleaned
1
2
3
4
5
9
17
24
30
35
Based on the above info, the marginal revenue from the fourth worker is
a. $6.
b. $ 30.
c. $150.
d. $750
e. none of the above
3-66 A housecleaning company receives $25 for each house cleaned. The table below gives the
relation between the number of workers and the number of houses that can be cleaned per week.
Number of Workers
Houses Cleaned
1
2
3
4
5
9
17
24
30
35
Based on the above info, if the company want to maximize profit and hires three workers, the
wage rate of a housecleaner can be no more than
a. $175.
b. $200.
c. $225.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
d. $600.
e. none of the above
3-67 A housecleaning company receives $25 for each house cleaned. The table below gives the
relation between the number of workers and the number of houses that can be cleaned per week.
Number of Workers
Houses Cleaned
1
2
3
4
5
9
17
24
30
35
Based on the above info, if the wage rate of a housecleaner is $130, what is the maximum amount
of profit the company can earn?
a. $ 20
b. $150
c. $230
d. $750
e. none of the above
3-68 A restaurant currently has two cooks and ten waiters. Cooks earn $10 an hour and waiters earn $5
an hour. The last cook added 40 meals served to total output, while the last waiter added 25 meals
served to total output. In order to maximize the number of meals served with a fixed budget, the
manager should
a. continue to use two cooks and ten waiters because output is being maximized.
b. should use more cooks and fewer waiters because cooks are more productive than
waiters.
c. should use more cooks and fewer waiters because productivity per dollar is higher for
cooks than for waiters.
d. should use more waiters and fewer cooks because waiters are paid less than cooks.
e. should use more waiters and fewer cooks because productivity per dollar is higher for
waiters than for cooks.
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
3-69 Randolph is taking three courses this semester: economics, statistics, and finance. He has decided
to spend 20 hours per week studying (in addition to attending all his classes) and his objective is
to maximize his average grade, which means maximizing the total of his grades in the three
courses. The table shows Randolph’s estimate of the relation between time spend studying and his
grade for each course.
Grade in:
Hours of study
Economics
Statistics
Finance
4
63
54
68
5
72
64
76
6
79
72
82
7
85
78
87
8
88
83
90
9
90
87
93
10
92
89
95
Based on the above info, how should Randolph allocate his time?
a. 7 hours economics, 7 hours statistics, 6 hours finance
b. 6 hours economics, 6 hours statistics, 8 hours finance
c. 7 hours economics, 6 hours statistics, 5 hours finance
d. 6 hours economics, 5 hours statistics, 7 hours finance
3-70 Randolph is taking three courses this semester: economics, statistics, and finance. He has decided
to spend 20 hours per week studying (in addition to attending all his classes) and his objective is
to maximize his average grade, which means maximizing the total of his grades in the three
courses. The table shows Randolph’s estimate of the relation between time spend studying and his
grade for each course.
Grade in:
Hours of study
Economics
Statistics
Finance
4
63
54
68
5
72
64
76
6
79
72
82
7
85
78
87
8
88
83
90
9
90
87
93
10
92
89
95
Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISION MAKING
Based on the above info, what is the maximum AVERAGE grade Randolph can earn if he studies
20 hours per week?
a. 80
b. 80.3
c. 82
d. 81.7
3-71 A package delivery service uses vans and employees to deliver the maximum number of packages
given a fixed budget. The last van added 600 packages to total output, while the last employee
added 500 packages. If vans cost $400 per week and employees earn $300 per week, the firm
a. could deliver more packages with the same budget by using more employees and fewer
vans.
b. could deliver more packages with the same budget by using more vans and fewer
employees.
c. should use more vans and fewer employees because the last dollar spent on vans added
more to total output than the last dollar spent on employees.
d. is delivering the maximum number of packages given the fixed budget.
e. both b and c
3-72 A grocery store hires cashiers and baggers. Cashiers earn $8 an hour; baggers earn $4 an hour.
The manager, who wants to maximize the number of customers served given a fixed payroll,
expects the following productivity from cashiers and baggers:
Total number of customers served
Number of employees
Cashiers
Baggers
1
2
3
4
5
240
440
600
712
776
136
264
384
496
560
Given the above information, with a payroll of $32 (per hour), how should the manager allocate
this budget?
a. Hire three cashiers and two baggers
b. Hire two cashiers and four baggers
c. Hire two cashiers and three baggers
d. Hire four cashiers and one bagger