Solution Manual
DmaH C. Newnan
J ~ e m P.
e Lavelle
Making Economic Decisions
Note p l e a s e t h a t t h e r e may be no a b s o l u t e answers t o t h e s e
q u e s t i o n s . The g o a l i s t o make s t u d e n t s t h i n k , r a t l ~ e rt h a n
t o g r a d e them on a Right-Wrong b a s i s .
A s u r v e y of s t u d e n t s answering t h i s q u e s t i o n i n d i c a t e d t h a t tlley
thought about 40% of t h e i r d e c i s i o n s were c o n s c i o u s d e c i s i o n s .
(a)
Yes.
The c h o i c e of an e n g i n e h a s i m p o r t a n t money consequences
s o would be s u i t a b l e f o r e n g i n e e r i n g economic a n a l y s i s .
(b)
Yes.
I m p o r t a n t economic - and s o c i a l - consequences.
Some might a r g u e t h e s o c i a l consequences a r e more
i m p o r t a n t t h a n t h e economics.
(c)
?
(d)
No.
P i c k i n g a c a r e e r on an economic b a s i s sounds t e r r i b l e .
(e)
No.
P i c k i n g a w i f e on an economic b a s i s sounds even worse.
Probably t h e r e a r e a v a r i e t y of c o n s i d e r a t i o n s much more
i m p o r t a n t t h a n t h e economics.
Of t h e t h r e e a l t e r n a t i v e s , ( b ) t h e $150,000 i n v e s t m e n t problem
is most s u i t a b l e f o r economic a n a l y s i s . There i s n o t enough d a t a
t o f i g u r e o u t how t o p r o c e e d , h u t i f t h e " d e s i r a b l e i n t e r e s t r a t e "
were 9 % , t h e n f o r e g o i n g i t f o r one week would mean a l o s s o f
1
G ( 0 . 0 9 ) = 0.0017 = 0 . 1 7 % immediately
I t would t a k e o v e r a y e a r a t 0 . 1 5 % more t o e q u a l t h e 0 . 1 7 % f o r e g o n e
now.
( a ) The candy b a r problem i s s u i t a b l e f o r economic a n a l y s i s .
Compared t o ( a ) , o f c o u r s e , i t i s t r i v i a l .
( c ) A r e a l problem w i t h s e r i o u s economic c o n s e q u e n c e s . The
d i f f i c u l t y may be i n f i g u r i n g o u t what one g a i n s i f t h e y pay
f o r t h e f e n d e r damage, i n s t e a d o f having t h e i n s u r a n c e company
pay f o r i t .
1-1
1-2
Chapter 1
Introduction
Gambling, the stock market, drilling for oi 1, hunting for buried
treasure - - - there are sure to be a lot of interesting answers.
Note that if you could double your money every day, then
2'($300)
= $1,000,000
and
x is less than 12 days.
Maybe their stock market "systems" don't work!
1-6
It may look simple to the owner because
is not the one losing
a job. For the three machinists it represents a major event with
major consequences.
For most high school seniors there probably are only a linited
number of colleges and universities that are feasible alternatives.
Nevertheless, it still is a complex problem.
I t really is not an rcononic problem - it is a complex problem.
Since it takes tine and effort to go to the bookstore, the minimum
number of pads might be related to the smallest saving worth
bothering about. The maximum number of pads might be the quantity
needed over a reasonable period of time, like the rest of the
academic year.
1-10
While there might be a lot of disagreement on the "correct" answer,
only 'dl [automobile insurance] represents a substantial ainount of
money and a situation where money might be the primary basis for
choosing between alternatives.
The student will have a hard
The overall problems are all comple::.
ti::~e coming up with examples Lhat are truly simple or intermediate
until he/slie breaks then into smaller and smaller subproblems.
Chapter 1
Introduction
T h e s e q u e s t i o n s w i l l c r e a t e d i s a g r e e m e n t . None o f t h e s i t u a t i o n s
represents r a t i o n a l decision-making.
( a ) C h o o s i n g t h e s l m e c a r e e r as a f r i e n d m i g h t b e O K , b u t i t
d o e s n ' t seein t o o r a t i o n a l .
(b) J i l l d i d n ' t c o n s i d e r a l l t h e a l t e r n a t i v e s .
( c ) Don t h o u g h t h e was m i n i m i z i n g c o s t , b u t i t d i d n ' t w o r k .
Maybe r a t i o n a l d e c i s i o n - m f k i n g s a y s o n e s h o u l d b u y b e t t e r
tools t h a t w i l l l a s t .
1-13 Possible objectives for NASA can be stated in general terms of space exploration or the
generation ofknowledge orthey can be stated in ver). concrete terms. President Kennedy used
the latter approach with a year for landing a man on the moon to inspire employees. Thus the
following objectives as examples are concrete. N o year is specitied here, because unlike
President Kennedy u e d o not know what dates may be achievable.
Land a man safely on Mars and return him to earth by
Establish a colony on the moon by
Establish a permanent space station by
.
Support private sector tourism in space by
.
Maximize fundamental knowledge about science through .x probes per year or for Sy
per year.
Maximize applied knowledge about supporting man's activities in space through x
probes per year or for 3). per year.
Choosing among these objectives involves technical decisions (some objectives rnay
be prerequisites for others). political decisions (balance between science and applied
knowledge for man's activities), and economic decisions (how many dollars per year can be
allocated to NASA).
However. my favorite is a colony on the moon, because a colony is intended to be
permanent and it would represent a new frontier for human ingenuity and opportunity.
Evaluation of alternatives would focus on costs, uncertainties, and schedules. Estimates of
these would rely on NASA's historical experience, expert judgement, and some o f the
estimating tools discussed in Chapter 2.
1-3
1-4
--
--
Chapter 1
Introduction
This i s a c h a l l e n g i n g q u e s t i o n . One approach might b e :
( a ) Find out what p e r c e n t a g e of t h e p o p u l a t i o n i s l e f t - h a n d e d .
(b) What i s t h e p o p u l a t i o n o f t h e s e l e c t e d home-town?
(c) Next, market r e s e a r c h might be r e q u i r e d . With some s p e c i f i c
s c i s s o r s ( q u a l i t y and p r i c e ) i n mind, ask a random sample o f
people i f t h e y would p u r c h a s e t h e s c i s s o r s . Study t h e
responses o f both l e f t - h a n d e d and right-handed p e o p l e .
j d j Kith only two hours a v a i l a b l e , t h i s i s probably a l l t h e
i n f o r m a t i o n one could c o l l e c t . From t h e d a t a , make an
estimate.
d i f f e r e n t approach might b e t o assume t h a t t h e p e o p l e i n t e r e s t e d
i n l e f t - h a n d e d s c i s s o r s i n t h e f u t u r e w i l l be about t h e same a s
t h e number who bought them i n t h e p a s t .
(a) Telephone s e v e r a l sewing and department s t o r e s i n t h e a r e a .
Ask two q u e s t i o n s :
1. How many p a i r s of s c i s s o r s have you s o l d i n one
y e a r ( o r s i x months o r ? ) .
2 . What i s t h e r a t i o o f s a l e s of l e f t - h a n d e d s c i s s o r s
t o regular scissors?
(b) From t h e d a t a i n ( a ) e s t i m a t e t h e f u t u r e demand f o r l e f t handed s c i s s o r s .
A
Two i t e m s might b e worth n o t i n g .
1.
2.
Lots of s c i s s ~ r sa r e u n i v e r s a l , and ~ : q u a l l y u s e f u l f o r l e f t
and r i g h t - h a n d e d people.
Many l e f t - h a n d e d p e o p l e p r o b a b l y n e v e r have heard of l e f t handed s c i s s o r s .
F e a s i b l e a l t e r n a t i v e s might i n c l u d e :
1.
2.
3.
4.
5.
Live a t home.
A room i n a p r i v a t e home i n r e t u r n f o r work i n t h e garden, e t c .
Become a Resident A s s i s t a n t i n a U n i v e r s i t y dormatory.
Live i n a camper - o r a t e n t - i n a nearby r u r a l a r e a .
Live i n a t r a i l e r on a c o n s t r u c t i o n s i t e i n r e t u r n f o r
"keeping an eye on t h e p l a c e . "
Chapter 1
1-5
Introduction
1-16
1-16 A common situation is looking for a car where the car is purchased from either the first
dealer or the most promising alternative from the newspaper's classified section. This may
lead to an acceptable or even a good choice, but it is highly unlikely to lead to the best choice.
A better search would begin with Consumer Reports or some other source that summarizes
many models of vehicles. While reading about models, the car buyer can be identifying
alternatives and clarifying which features are important. With this in mind, several car lots can
be visited to see many of the choices. Then either a dealer or the classifieds can be used to
select the best alternative.
"choose t h e b e t t e r o f t h e u n d e s i r a b l e a l t e r n a t i v e s . "
A.
B.
C.
D.
A.
B.
C.
D.
Maximize
Minimize
Maximize
Minimize
Maximize
Maximize
Minimize
Minimize
t h e d i f f e r e n c e between o u t p u t and i n p u t
input
t h e d i f f e r e n c e between o u t p u t and i n p u t
input
t h e d i f f e r e n c e between o u t p u t and i n p u t
t h e d i f f e r e n c e between o u t p u t and i n p u t
input
input
Some p o s s i b l e answers a r e :
There a r e b e n e f i t s t o t h o s e who g a i n from t h e d e c i s i o n ,
b u t n o one i s harmed. [ P a r e t o Optimum)
B e n e f i t s flow t o t h o s e who need them most. (Welfare c r i t e r i o n )
Minimize a i r p o l l u t i o n o r o t h e r s p e c i f i c i t e m .
Maximize t o t a l employment on t h e p r o j e c t .
Maximize pay and b e n e f i t s f o r some group. ( e . g . , u n i o n
members)
Most a e s t h e t i c a l l y p l e a s i n g r e s u l t .
F i t i n t o normal workweek t o a v o i d o v e r t i m e .
Maximize t h e u s e o f t h e p e o p l e a l r e a d y w i t h i n t h e company.
1-6
Chapter 1
Introduction
S u r e l y p l a n n e r s would l i k e t o u s e c r i t e r i o n ( a ) . U n f o r t u n a t e l y ,
p e o p l e who a r e r e l o c a t e d o f t e n f e e l harmed, n o m a t t e r how much
money, e t c . , t h e y a r e g i v e n . Thus p l a n n e r s c o n s i d e r c r i t e r i o n ( a )
unworkable and u s e c r i t e r i o n ( b ) i n s t e a d .
1-22 In this kind of highway project, the benefits typically focus on better serving future
demand for travel measured in vehicles per day, lower accident rates, and time lost due to
congestion. In some cases, these projects are also used for urban renewal of decayed
residential or industria1 areas, which introduces other benefits.
The costs of these projects include the money spent on the project, the time lost by
travelers due to construction caused congestion, and the lost residences and businesses of
those displaced. In some cases, the loss may be intangible as a road separates a neighborhood
into two pieces. In other cases, the loss may be due to living next to a source of air, noise, and
visual pollution.
The remaining costs for the year are:
Alternative:
1. To stay in the dormitory the rest of the year
Food: 8 months at $120/month
2.
=
To stay in the dormitory the balance of the
first semester; apartment for second semester
Housing: 44 months x $80 apartment - $190 dorm =
Food :
34 months x $120 + 44 x $100
=
$960
170
870
$1040
3
Move into an apartment now
Housing: 8 mo x $80 apartment - 8 x $30 dorm
Food :
8 mo x $100
=
=
400
800
$1200
Ironically, Ja:, had sufficient money to live in an apartment
all year. He originally had $1770($1050 + 1 mo dorm food of $120
plus $600 dorm contract cost). His cost for an apartment for the
year would have been 9 mo x ($80 + $100) = $1620.
Alternative 3 is not possible for the cost exceeds Jay's $1050.
Jay appears to prefer Alt. 2, and he has sufficient money to adopt it
Chapter 1
Introduction
1-7
1-24
"in d e c i s i o n - m a k i n g t h e model i s m a t h e m a t i c a l . "
The s i t u a t i o n i s an example
may have major consequences
are alternatives available,
d i s c a r d e d t h e r e s t and a s k s
o f t h e f a i l u r e o f a low c o s t i t e m t h a t
i n a p r o d u c t i o n s i t u a t i o n . While t h e r e
one a p p e a r s s o obvious t h a t t h e foreman
t o proceed with t h e replacement.
One c o u l d a r g u e t h a t t h e foreman, o r t h e p l a n t manager, o r b o t h a r e
making d e c i s i o n s . There i s no s i n g l e " r i g h t " answer t o t h i s problem.
While everyone might n o t a g r e e , t h e key d e c i s i o n seems t o b e i n
p r o v i d i n g B i l l ' s Dad an o p p o r t u n i t y t o judge between p u r p o s e l y
l i m i t e d a l t e r n a t i v e s . Although s u g g e s t e d by t h e c l e r k , i t was B i l l ' s
decision.
[One of my s t u d e n t s o b s e r v e d t h a t h i s F a t h e r would n o t f a l l f o r such
a s i m p l e d e c e p t i o n , and s u r e l y would i n s i s t on t h e w e i r d s h i r t a s
a s u b t l e form o f p u n i s h m e n t . ]
Plan A
B
C
C
P r o f i t = Income - Cost = $800 - 600 = $ 2 0 0 / a c r e
P r o f i t = $1900 - $1500 = $ 4 0 0 / a c r e
P r o f i t = 2250 - 1800 = $ 4 5 0 / a c r e
P r o f i t = 2500
2100 = $ 4 0 0 / a c r e
To maximize p r o f i t p e r a c r e , s e l e c t P l n n C .
-
1-8
Chapter 1
Introduction
1-28 Each student's answer will be unique, but there are likely to be common threads.
Alternatives to their current major are likely to focus on other fields of engineering and
science, but answers are likely to be distributed over most fields offered by the university.
Outcomes include degree switches, courses taken, changing dates for expected graduation, and
probable future job opportunities.
At best criteria will focus on joy in the subject matter and a good match for the
working environment that pleases that particular student. Often economic criteria will be
mentioned, but these are more telling when comparing engineering with the liberal arts that
when comparingengineeringfields. Other criteria may revolve around an inspirational teacher
or an influential friend or family member. In some cases, simple availability is a driver. What
degree programs are available at a campus or which programs will admit a student with a 2.xx
(;PA in first year engineering.
At best the process will follow the steps outlined in this chapter. At the other extreme,
a student's major may have been selected by the parent and may be completely mismatched
to the student's interests and abilities.
Students shouldn't lightly abandon a major, as changing majors represents real costs
in time, money, and effort and real risks that the new choice will be no better a fit.
Nevertheless, it is a large mistake to not change majors when a student now realizes the major
is not for them.
1-29 The most common large problem faced by undergraduate engineering students is where
to look for a job and which offer to accept. This problem seems ideal for listing student ideas
on the board or overhead transparencies. It also a good opportunity for the instructor to add
more experienced comments.
T e s t m a r k e t i n g a n d p i l o t p l i ~ n t o p e r a t i o n a r e s i t u a t i o n s where i t i s
hoped t h a t s o l v i n g t h e s u b p r o b l e m s g i v e s a s o l u t i o n t o t h e l a r g e r
o v e r a l l problem.
On t h e o t h e r h a n d , Example 3-1 ( s h i p p i n g d e p t .
buying p r i n t i n g ) i s a s i t u a t i o n where t h e subproblem does n o t l e a d
t o a p r o p e r complex p r o b l e m s o l u t i o n .
Chapter 1
Introduction
1-9
1-31
(a)
The s u i t a b l e c r i t e r i o n i s t o maximize t h e d i f f e r e n c e between
o u t p u t and i n p u t . O r s i m p l y , maximize n e t p r o f i t .
The d a t a from t h e g r a p h s may be t a b u l a t e d a s f o l l o w s :
Output
Units/hour
50
100
150200
250
Total Total
Net
Cost Income P r o f i t
$300 $800
500 1000
700 -1350
1400 1600
2000 1750
$500
500
650
200
-250
- -Best
P r o d u c t i o n Rate
Output ( U n i t s / h o u r )
(b)
Minimum i n p u t i s , o f c o u r s e , z e r o and maximum o u t p u t i s
250 u n i t s / h r (based on t h e g r a p h ) . S i n c e one cannot a c h i e v e
maximum o u t p u t a t minimum i n p u t , t h e s t a t e m e n t makes no s e n s e .
1-10
Chapter 1
introduction
I t e m i z e d F i p e n s e s : $0.123 x 1 8 , 0 0 0 m i l e s + 52000
Based on S t a n d a r d M i l e a g e R a t e :
$0.22 x 18,009
=
=
$4214
3960
Itemizing produces a l a r g e r r c j m b u r s e ~ e n t
Breakeven:
Let x
=
x=-
m i l e a g e a t which b o t h methods y i e l d t h e
same amount
$2000
$0.22 - $0.123
=
20,619 m i l e s
The f u n d a m e n t a l c o n c e p t h e r e i s t h a t we w i l l t r a d e a h o u r o f s t u d y
i n one s u b j e c t f o r an h o u r o f s t u d y i n a n o t h e r s u b j e c t s o l o n g a s
we a r e i m p r o v i n g t h e t o t a l r e s u l t s . The s t a t e d c r i t e r i o n i s t o
" g e t a s h i g h an a v e r a g e g r a d e a s p o s s i b l e i n t h e combined c l a s s e s . "
[ T h i s i s t h e same a s s a y i n g " g e t t h e h i g h e s t combined t o t a l s c o r e . " ]
S i n c e t h e d a t a i n t h e problem i n d i c a t e t h a t a d d i t i o n a l s t u d y always
i n c r e a s e s t h e g r a d e , t h e q u e s t i o n i s how t o a p p o r t i o n t h e a v a i l a b l e
15 h o u r s o f s t u d y among t h e c o u r s e s . One m i g h t b e g i n , f o r e x a m p l e ,
a s s u m i n g f i v e h o u r s o f s t u d y on e a c h c o u r s e . The combined t o t a l
s c o r e would b e 1 9 0 .
D e c r e a s i n g t h e s t u d y o f m a t h e m a t i c s one h o u r would r e d u c e t h e math
g r a d e by 8 p o i n t s ( f r o m 52 t o 4 4 ) . T h i s h o u r c o u l d b e u s e d t o
i n c r e a s e t h e p h y s i c s g r a d e by 9 p o i n t s ( f r o m 59 t o 6 8 ) . The r e s u l t
would b e :
4 hours
44
Math
68
Physics
6 hours
E n g r Econ
5 hours
191
2
F u r t h e r s t u d y would show t h a t t h e b e s t u s e o f t h e t i m e i s :
Math
Physics
E n g r Econ
4 hours
7 hours
4 hours
44
77
2
192
Chapter 1
Introduction
1-1 1
1-35
Area
A
p r e p a r a t i o n c o s t = 2 x 106 u $ 2 . 3 5
Area
B
Difference i n haul
0.60 x 5 miles = 3.0
0 . 2 0 x -2 m i = - 0 . 4
0
0.20 x 0
2.6
=
$4,700,000
miles
miles
miles
miles average addnl haul
mi x $ 3 5 / h r
Cost o f a d d i t i o n a l h a u l p e r load = 15 mph
S i n c e t r u c k c a p a c i t y = 20 m
3
=
$6.07
3
A d d i t i o n a l c o s t / c u b i c y a r d = $6.07120 m3
=
$0.303/m
For 14 m i l l i o n c u b i c m e t e r s :
T o t a l Cost
Area
B
=
14 x l o 6 x $ 0 . 3 0 3
=
$4,240,000
w i t h i t s lower t o t a l c o s t i s p r e f e r r e d .
3000 g a l l o n c a p a c i t y =
7 . 4 8 gal,cf
3000
=
401 c u b i c f e e t c a p a c i t y
Let L = t a n k l e n g t h i n f e e t
d = tank diameter i n f e e t
The volume o f a c y l i n d r i c a l t a n k e q u a l s t h e end a r e a x t h e l e n g t h
401 x 4
Volume = - d 2t = 401 c f o r L = 4
n
d2
The t o t a l s u r f a c e a r e a = two end a r e a s + t h e c y l i n d e r s u r f a c e a r e a
S u b s t i t u t e i n t h e equation f o r L
Take t h e f i r s t d e r i v a t i v e and s e t i t e q u a l t o z e r o
S u b s t i t u t e back f o r L
1-12
Chapter 1
Introduction
Quantity sold
p e r week
Selling
price
300 packages
60 $
$180
Cost
$105
600
45
2 70
2 10
60
1200
40
4 80
3 36
144
Income
-
Profit
$ 75
*buy 1700 packages a t 254 each
**buy 2000 packages a t 20$ each
C o n c l u s i o n : Buy 2000 packages
S e l l a t 334 each
Ti me
o
o
Daily s a l e s
in i
p o d
Costof
gr;c;;ies
Hourly
Hourly
;O;i
p;;:it
The f i r s t p r o f i t a b l e o p e r a t i o n i s i n t h e 0700-0800 t i m e p e r i o d .
In t h e e v e n i n g t h e 2200-2300 time p e r i o d i s u n p r o f i t a b l e , b u t
n e x t h o u r ' s p r o f i t more t h a n makes up f o r i t .
Conclusion:
Open a t 0700
C l o s e a t 2400
Chapter 1
1-1 3
Introduction
1-39
Occupancy
Rate No. rooms
Net
Income
100%
50
$1200
30
94
47
1410
48
36
80
40
1440
4
54
42
66
33
1386
5
48
36
70
35
1260
6
54
42
68
34
1428
7
62
50
66
33
1650
8
68
56
56
28
1568
Alternative
Price
Net income
p e r room
1
$36
$24
2
42
3
To maximize n e t income, Joy s h o u l d n o t a d v e r t i s e and c h a r g e
$62 p e r n i g h t .
P r o f i t = Income
-
Cost
where PQ = 35Q - 0.02Q2
= PQ - C
C = 44 + 8000
P r o f i t = 354
= 314
d2 ( P r o f i t )
dQ2
-
0.02Q2
-
44 - 8000
0 . 0 2 ~- ~8000
= -0.04
The n e g a t i v e s i g n i n d i c a t e s t h a t p r o f i t
i s a maximum a t Q e q u a l s 775 u n i t s l y e a r .
Answer: Q = 775 u n i t s l y e a r
I - IJ
-
-.
C llapter 1
Introduction
Chapter 2 Engineering Costs and Cost Estimating
1-41
CHAPTER
2-1
2
Engineering Costs
and Cost Estimating
L e t t = t i m e from t h e p r e s e n t ( i n w e e k s )
Volume of a p p l e s a t a n y t i m e = ( 1 0 0 0 + 1 2 0 t - 2 0 t )
P r i c e a t any time = 3.00 - 0 . 1 5 t
T o t a l C a s h R e t u r n (TCR)
=
=
This i s an example o f a "sunk c o s t . " The $4000 i s a p a s t c o s t and
should n o t be allowed t o a l t e r a s u b s e q u e n t d e c i s i o n u n l e s s t h e r e
i s some r e a l - o r p e r c e i v e d - a f f e c t . S i n c e e i t h e r home i s r e a l l y
an i n d i v i d u a l p l a n s e l e c t e d by t h e homeowner, each should be judged
i n terms o f v a l u e t o t h e homeowner v s . t h e c o s t . On t h i s b a s i s t h e
s t o c k p l a n house a p p e a r s t o b e t h e p r e f e r r e d a l t e r n a t i v e .
(1000 + 120t - 2 0 t ) ( 3 . 0 0 - 0 . 1 5 t )
3000 + 1 5 0 t - 1 5 t 2
T h i s i s a minima-maxima p r o b l e m .
S e t t h e f i r s t d e r i v a t i v e e q u a l t o z e r o and s o l v e f o r t .
dTCR
-
dt
-d'TCR
=
-10
dt2
At t
150
=
-
30t = 0
- 5 weeks
t = - -30
(The n e g a t i v e s i g n i n d i c a t e s t h e f u n c t i o n i s a
maximum f o r t h c c r i t i c a l v a l u e . )
5 weeks:
T o t 2 . l Zash R e t u r n (TCR)
=
3000
+
1 5 0 ( 5 ) - ~ 5 ( 5 =) ~$3375
(a)
Monthly Bill:
50x30=
1500 kw-hr @ $0.086
1300 kw-hr $0.066
kw-hr
2800
8
=
$129.00
$ 85.80
$ 214.80
Average Cost = 2 14.8012800= $0.0767 per kw-hr
Marginal Cost (cost for the next kw-hr) = $ 0.066 because the 2801" kw-hr is in the 2" bracket
ofll~ecost structure
t $0.066 for l SO I-10-3000kw-hr)