Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Answer the question.
1)
The cost of standard lithography equipment with a capacity of 170 circuit boards per hour
is $5700. If the cost for custom lithography equipment with a capacity of 185 circuit boards
per hour is $6900, what is the value of the exponent in the cost–capacity equation?
1)
Answer:
2.26
Explanation:
CA=CBSA
SB
x
$6900 =$5700(185/170)x
1.2105 =1.0882x
log (1.2105)= x log (1.0882)
x=2.26
2)
The cost of construction for a hydrogen plant with a capacity of 7000 standard cubic feet
per day (scfd) was $10 million ten years ago, when the current construction cost index was
4535. If the index increased at an average rate of 6.8% per year for the past ten years, what
would a(n) 12,000–scfd plant with a similar design be expected to cost now? Use the
cost–capacity exponent of 0.56.
2)
Answer:
$26,109,534.10
Explanation:
CA=CBIn
Ik
SA
SB
x
= (10,000,000)(1.068)10(12,000/7000)0.56
=$26,109,534.10
3)
The cost of an aerobic digester system with a capacity of 140 million gallons per day
(MGD) is $2.1 million. If the cost–capacity exponent is 0.14, what would be the expected
cost of a 440–MGD system?
3)
Answer:
$2,465,157.91
Explanation:
C2=$2,100,000(440/140)0.14
=$2,465,157.91
1
4)
What is the estimate of the cumulative average hours per unit required to produce the 5th
unit of a production run that has a(n) 78% learning curve, if the first unit takes 50 hours?
4)
Answer:
36.25 hours
Explanation:
C5=T5/5
T5=50 5
u=1ulog(0.78)/log2
=181.23 hours
C5=181.23/5
=36.25 hours
5)
A property manager wants to estimate the annual costs of window cleaning for a newly
acquired office building. She collected the following information related to costs of the 10
properties she currently manages:
xi=17,470 x2
i=34,125,100, where x is the window surface (ft2)
yi=1,350,955 y2
i=203,605,360,640 and xiyi=2,635,901,696, where y is the
cleaning costs
Determine a CER equation for the cleaning costs and the correlation coefficient.
5)
Answer:
y =1450.000 +76.500x
Correlation coefficient =1.0000
Explanation:
x= ( xi)/n=1747; y= ( yi/n) =135,095.5
b1=2,635,901,696 – (1747)(1,350,955)
34,125,100 – (1747)(17,470)=76.500
b0=135,095.5 – (76.500)(1747)
=1450.000
y =1450.000 +76.500x
R =Sxy
SxxSyy; Sxy =2,635,901,696 – (17,470)(1,350,955)/10 =275,783,311.000
Sxx =34,125,100 –(17,470)2/10 =3,605,010.000
Syy =203,605,360,640 –(1,350,955)2/10 =21,097,419,437.500
Thus, R =275,783,311.000
(3,605,010.000)(21,097,419,437.500)
=1.0000
2
6)
A new entrepreneur wants to estimate the costs of an offsite team–building event for her 14
employees. She was able to gather the following information on a 3–day program in
which she is interested. Use the unit technique to estimate the cost per employee of this
event. Assume there will 100% participation in all activities.
Cost Elements Cost Rate
Transportation costs
(The site is 60 miles away.) Van rental of $109 pay day per 14 people.
The van gets 16 mpg and the gas is $3.10 per gallon.
Insurance costs $24 per person.
Accommodation costs
(for 3 days and 3 nights) A double–bed room holds 2 people and has a rate of $119 per night
per room.
Meals are $45 per day per person.
A conference room costs $180 per day for a karaoke night
Activities costs A paintball game costs $55 per person.
A night journey and a day hike, each costs $35 per person.
A problem–solving and team–building exercise costs $160 per
14 people.
A karaoke night costs $230 per 14 people for equipment and a DJ.
6)
Answer:
$7395.25
Explanation:
Transportation costs =$109/day x 3 days + $2 x 60 mile/16 mpg x $3.10/ gallon +
$24/person x 14 =$686.25
Accommodation costs =$119/night x 3 nights x 14/2 rooms +$45 x 3 days x 14 +
$180 =$4569.00
Activities costs = $(55 + 2x(35))/person x 14 person +$160 +$230 =$2140.00
Total costs =$686.25 +$4569.00 +$2140.00
=$7395.25
3
7)
An autoclaves and sterilizers manufacturer has estimated the manufacturing costs of its
new product as follows:
Cost Elements Cost Rate
Direct labor $20 per hour
Material $270 per unit
Overhead costs 110% of direct labor
The company’s engineer estimated that the production of the new product has a 88%
learning curve applied to labor required, and the time to complete the first unit was 54
labor hours. Assume the time required to complete the 10th unit and the competitor’s
price of $2053.44 per unit are used for cost estimation purposes. What is the maximum
profit margin for the company to remain competitive?
7)
Answer:
17.00%
Explanation:
The estimate of direct labor hours is based on the time to produce the 10th unit.
n = (log 0.88)/(log 2) = –0.1844
Z10 = (54)(10)–0.1844 =35.32 hours per unit
Direct labor = ($20/hour)(35.32 hours/unit) =$706.40/unit
Material =$270/unit
Overhead = (1.1)($706.40/unit) =$777.04 /unit
Total manufacturing cost =$1753.44/unit
Maximum profit =$2053.44–$1753.44
=$300.00/unit
Profit margin =$300.00/$1753.44 =$0.17 or 17.00%
8)
An assembly task has a learning curve rate of 93% and reaches a steady state after 70 units
with 15 man–hours per unit. What is the estimated number of man–hours required to
complete the first and the fifth units?
8)
Answer:
23.40 man–hours for the first unit
19.77 man–hours for the fifth unit
Explanation:
Z70 =Kun
15 =K(70)log0.93/log 2
K = (23.40) man–hours for the first unit
Z5= (23.40)(5)log0.93/log 2
=19.77 man–hours for the fifth unit
9)
The cost of carbon dioxide (CO2) lasers that are used in welding and marking applications
was $6000 when the index was 175. What will be the estimated cost of the replacement
when the index is 230?
9)
Answer:
$7885.71
Explanation:
Cn=CkIn
Ik=$6000 230
175 =$7885.71
4
10)
Your boss asked you to estimate the required number of units sold to achieve a profit of
$26,500 per year. Currently, the product is sold at $1800 per unit. You have collected the
following information:
Cost Elements Cost Rate
Direct labor 40 hours per batch of 60 units
Direct labor costs $60 per hour
Material costs $5100 per batch of 60 units
Overhead costs 125% of direct labor
Quality control 45% of direct labor
Packaging and shipping $33 per unit
If the units sold must account for total production costs and desired profit, how many units
of production would you recommend to your boss?
Answer:
16.84 units
Explanation:
Let p = units sold
Revenue =$1800p
Labor cost = $(40/60)/unit x p x $60=$40.00p
Material cost = $(5100/60)/unit) x p =$85.00p
Overhead cost = $(1.25)(40.00p) =50.00p
Quality Control cost = $(0.45)(40.00p) =18.00p
Packaging cost =$33p
Total cost =$226p
=$226.00p
Profit = Revenue – Cost
$26,500 =$1800p –$226.00p
=1574.00p
p =26,500/1574.00
=16.84 units
5
11)
An industrial engineer, who was formerly a real estate developer, wants to estimate the
construction costs of an apartment complex that he recently acquired. He gathered the
following information:
Cost Element Percent Index
Reference Year
($/ft2)
Index
Current Year
($/ft2)
Studio units 546 69
One bedroom units 17 75 107
Two bedroom units 30 150 192
Three bedroom units 23 175 202
Four bedroom units 21 170 198
Central facilities and landscaping 4100 120
If the total construction cost of the similar property was $2.5 million in the reference year,
what is his estimated construction cost in the current year?
Answer:
$3,073,214.29
Explanation:
IR= 0.05(46) + 0.17(75) + … + 0.04(100)
=140.0
IC= 0.05(69) + 0.17(107) + … + 0.04(120)
=172.1
Cc =2,500,000 172.1
140.0
=$3,073,214.29
6
12)
To investigate operating costs, a commercial trucks owner has prepared the following
information related to costs of the last 10 jobs:
xi=7500 x2
i=6,450,000, where x is the driving distances of a shipment
(miles)
yi=127,550 y2
i=1,788,600,192 and xiyi=107,212,496, where y is the
operating costs
Determine a CER equation for the operating costs, and estimate the cost of the 700–mile
shipment.
Answer:
y =2255.000 +14.000x
Cost =$12,055.00
Explanation:
x= ( xi)/n=750; y= ( yi/n) =12,755
b1=107,212,496 – (750)(127,550)
6,450,000 – (750)(7500)=14.000
b0=12,755 – (14.000)(750)
=2255.000
y =2255.000 +14.000x
Thus, the estimated cost for the 700–mile shipment is:
Cost =$2255.000+ $(14.000)(700)
=$12,055.00
13)
An activated sludge plant cost $75 million when it was built in 1995. The detailed cost
breakdown is given below. Determine a weighted index for the construction of a similar
plant in 2009.
Cost Element Percent Index (1995) Index (2009)
Feasibility study and design services 565 105
Labor 30 170 226
Materials 40 180 227
Equipments including installation costs 25 105 137
Answer:
1.3
Explanation:
In=W1(Cn1/Ck1) +W2(Cn2/Ck2) +W3(Cn3/Ck3) +W4(Cn4/Ck4)
W1+W2+W3+W4
= (0.05)(105/65) + (0.30)(226/170) + (0.4)(227/180) + (0.25)(137/105)
=1.3
7
14)
The costs of manufacturing horizontal fixed–mount barcode scanners are as follows:
Cost Elements Cost Rate
Direct labor $24.5 per hour
Material $380 per 70 units
Overhead costs 150% of direct labor
The production has a 89% learning curve applied to labor required, and the time to
complete the first unit was 37 direct labor hours. Determine the unit selling price based on
the estimated time to complete the 100th unit, if the company wants a profit margin of 10%
based on total manufacturing costs.
Answer:
$1155.40
Explanation:
The estimate of direct labor hours is based on the time to produce the 100th unit.
n = (log 0.89)/(log 2) = –0.1681
Z100= (37)(100)–0.1681 =17.06 hours
Direct labor costs =$24.5 x 17.06=$417.97 per unit
Material cost = $(380/70) =$5.43 per unit
Overhead cost =1.50 x $417.97
=$626.96 per unit
Total manufacturing cost =$1050.36 per unit
Desired profit = (0.10)($1050.36)
=$105.04 per unit
Unit selling price =$1050.36 +$105.04
=$1155.40
15)
If 17 man–hours are needed to complete the 5th replication of a certain task and 12
man–hours are needed to complete the 10th replication, what is the learning–curve
parameter for this task?
Answer:
71%
Explanation:
Y5=17 =Y1(5)n
Y10 =12 =Y1(10)n
Thus, 17
12 =(5/10)n
1.4167 =(0.5)n
log 1.4167 = n log (0.5)
n= –0.503
Because n = log s/log 2
–0.503 = log s/0.30103
log s = –0.1514
s=0.71 or 71%
8
Answer Key
Testname: C3
1)
2.26
2)
$26,109,534.10
3)
$2,465,157.91
4)
36.25 hours
5)
y =1450.000 +76.500x
Correlation coefficient =1.0000
6)
$7395.25
7)
17.00%
8)
23.40 man–hours for the first unit
19.77 man–hours for the fifth unit
9)
$7885.71
10)
16.84 units
11)
$3,073,214.29
12)
y =2255.000 +14.000x
Cost =$12,055.00
13)
1.3
14)
$1155.40
15)
71%