Question 1 – Project Management (6 points)
Here are the precedence requirements,
normal and crash activity times, and normal and crash costs for a project:

Activity

Crash
Cost

Normal
Cost

Normal
Time

Crash
Time*

Cost
Per Week

Weeks

Preceding
relationship

A

$8000

$7000

7

6

$1000

1

—

B

$7000

$5000

3

2

$2000

1

A

C

$10200

$9000

4

3

$1200

1

A

D

$4500

$3000

5

4

$1500

1

B,C

E

$3000

$2000

2

1

$1000

1

D

F

$7000

$4000

4

2

$1500

2

D

G

$8000

$5000

5

4

$3000

1

E,F

*Crash Time is the fastest time we can
finish the job. Of course, in order to finish the job in quickest way possible
we have to spend as much as possible.
(Part A) What
are the critical path, the estimated normal completion time,
and estimated normal completion cost? (3 Points)
(Part
B) To shorten the project by four weeks,
which tasks would be shorten and what would the final total project cost be?
(Show your work completely) (3 Points)

Question 2 – Cheap Retailers (6 points)
The following table shows financial data
(year 2006) for Dirt Cheap Wholesale and Kwiki-Mart, two US retailers.

DIRT CHEAP
WHOLESALE

KWIKI-MART
STORES

Inventories
($MM)

4754

40894

Sales (net
$MM)

59217

397206

COGS ($MM)

52762

326606

Assume that both
companies have an average annual holding cost rate of 20% (i.e. it costs both
retailers $2 to hold an item that they procured for $10 for one entire year).
(Part A) How many days, on average, does a product stay in Dirt Cheaps
inventory before it is sold? Assume that stores operate 365 days a year. (3 Points)
(Part B) How much lower (expressed in $s) is, on average, the inventory
cost for Dirt Cheap compared to Kwiki-Mart of a house hold cleaner valued at $5
COGS? Assume that the unit cost of the house hold cleaner is the same for both
companies and that the price and the inventory turns of an item are
independent. (3 Points)

Question 3 – Old
City Photographics (6+1 points)
Located
alongside a cobblestoned street in Old City, Old City Photographics (OCP)
specializes in the processing of the traditional 35mm negative film, a once
dominant photographic medium now in decline due to the popularity of digital
photography. OCP offers three packages
to their customers. With the standard
package, the customer gets a set of 6×4 prints for $19.99. The deluxe package adds to the standard
package a CD-ROM of high resolution scans of the pictures for $29.99. Finally, the $39.99 pro package is similar to
the deluxe package in that it comes with a CD-ROM, although the customer gets a
contact print rather than a set of prints.
(A contact print is an 8×10 sheet of photographic paper that has all
pictures on the roll of film printed next to each other at reduced dimensions
and is used as an index.) The workflow
for OCP is shown below (s=standard, d=deluxe, p=pro):
.jpg” alt=”OPC pfd”>
OCP is operated by one person at every
station.
(Part A) On average, OCP receive 13 jobs
per hour consisted of 44% standard, 37% deluxe and 19% pro.
Which of the following statement best describes OCPs process? (3
Points)
a.
The process is demand-constrained
(implied utilization is less than 1.0 at
all steps)
b.
The process is
capacity-constrained and process film is the bottleneck
c.
The process is
capacity-constrained and scan film is the bottleneck
d.
The process is
capacity-constrained and make 6×4 prints is the bottleneck
e. The process is capacity-constrained and make
contact print is the bottleneck

(Part B) What is the implied utilization
(ratio of workload relative to capacity) at Scan Film (2 Points)
a.
less than 50%
b.
50% to 60%
c.
60% to 70%
d.
80% to 90%
e.
90% to 100%
f.
more than 100%
Justify your answer:

(Part C)
Fixing the relative proportions of job types, what is the largest number of
jobs per hour that OCP can handle?
Circle the answer closest to the correct answer. (2 Points)
a.
10
b.
11
c.
12
d.
14
e.
16
f.
18
Justify your answer:
question 4 – The right to vote (and not to wait) (6+1
points)

In the previous
two presidential elections in the United States, very long wait times have been
witnessed at precincts (voting stations) in states that ultimately decided the
election (Florida in 2000 and Ohio in 2004).
In Philadelphia as well, some voters
complained about the long lines in some precincts, with most complaints coming
from precinct A. In 2004, the average number of voters arriving at Precinct A
was of 35 per hour and the arrivals of voters was random with inter-arrival
times that had a coefficient of variation of 1 (CVa=1).
Philadelphia had
deployed 1 voting machine in Precinct A. Suppose that each voter spent on
average 100 seconds in the voting booth (this is the time needed to cast
her/his vote using a voting machine), with a standard deviation of 120 seconds.
(Part A) How
long on average a voter had to wait in line precinct at A in 2004 before entering in a booth to cast
her/his vote. Circle the closest answer. (3 Points)
a.
56 minutes
b.
58 minutes
c.
60 minutes
d.
62 minutes
e.
71 minutes
f.
75 minutes
g.
There is not sufficient information to answer
the question
Justify your answer:

Given the long
wait times for Precinct A, the city of Philadelphia is thinking of alternative
solutions to improve voting conditions. One of the proposed solutions is as
follows.
Proposal 1:
Deploy an additional voting machine in precinct A. Assume that the voter
turnout is expected to have similar characteristics in 2008 as in the previous
election.
(Part B) Under
Proposal 1, how long on average would a voter have to wait in line in precinct
A in 2008 before casting her/his vote. Circle the closest answer. (2 Points)
a.
1 minute
b.
5 minutes
c.
6 minutes
d.
10 minutes
e.
11 minutes
f.
There is not sufficient
information to answer the question
Justify your answer:

(Part C) Under Proposal 1, on average,
at precinct A, what would be the ratio of the average number of people voting
(at a booth) over the average number of people in the line (waiting). Circle
the closest answer. (2 Points)
a.
0.4
b.
1.4
c.
2.4
d.
3.4
e.
4.4
f.
5.4
g.
There is not sufficient
information to answer the question
Justify your answer:

question 5 – cranberries
again! (6+1 points)
At OPLOG
Cranberry Cooperation (OCC!) cranberries arrive on truck at a rate of 150
barrels per hour. The inventory of OCC consists of three different levels. The
very first level can hold up to 200 barrels of cranberry. The second level can
hold up to 180 barrels of cranberry. The third level has unlimited
capacity. Assume the first level of
inventory is filled before the second level and
the second level is filled before the third level.
The trucks
arrive uniformly from 6:00 AM to 2:00 PM. The OCC has three different groups of
workers. The first group start working at 6:30 AM and leave only if all the
inventory is processed. The first team of workers process cranberries at the
rate of 100 barrels per hour. The second group of workers join the first group
only if there are some cranberries left in the second level of inventory. Once
the second group join the first group, the cranberries will be processed at the
rate of 120 barrels per hour. The third group of workers join the second and
the first group only if they see some inventory in the third level. Once the
third group join the first two groups of workers, the cranberries are going to
be processed at the rate of 140 barrels per hour.
(Part
A) What time will the second group of workers start
working? (1 Point)
(Part
B) At what time(s) are there exactly 320 barrels of
cranberry in inventory ? (3 Points)
(Part C) At
what time would OCC finish processing the cranberries. (3 Points)
Bonus Question (1
point)

.manhattangmat.com/forums/how-many-zeros-does-100-end-with-t5008.html”>How many
zeros does 100! end with?
Question 1 – Project Management (6 points)Here are the precedence requirements,
normal and crash activity times, and normal and crash costs for a project:ActivityCrash
CostNormal
CostNormal
TimeCrash
Time*Cost
Per WeekWeeksPreceding
relationshipA$8000$700076$10001—B$7000$500032$20001AC$10200$900043$12001AD$4500$300054$15001B,CE$3000$200021$10001DF$7000$400042$15002DG$8000$500054$30001E,F*Crash Time is the fastest time we can
finish the job. Of course, in order to finish the job in quickest way possible
we have to spend as much as possible.(Part A) What
are the critical path, the estimated normal completion time,
and estimated normal completion cost? (3 Points) (Part
B) To shorten the project by four weeks,
which tasks would be shorten and what would the final total project cost be?
(Show your work completely) (3 Points)Question 2 – Cheap Retailers (6 points)The following table shows financial data
(year 2006) for Dirt Cheap Wholesale and Kwiki-Mart, two US retailers.DIRT CHEAP
WHOLESALEKWIKI-MART
STORESInventories
($MM)475440894Sales (net
$MM)59217397206COGS ($MM)52762326606Assume that both
companies have an average annual holding cost rate of 20% (i.e. it costs both
retailers $2 to hold an item that they procured for $10 for one entire year).(Part A) How many days, on average, does a product stay in Dirt Cheaps
inventory before it is sold? Assume that stores operate 365 days a year. (3 Points)(Part B) How much lower (expressed in $s) is, on average, the inventory
cost for Dirt Cheap compared to Kwiki-Mart of a house hold cleaner valued at $5
COGS? Assume that the unit cost of the house hold cleaner is the same for both
companies and that the price and the inventory turns of an item are
independent. (3 Points)Question 3 – Old
City Photographics (6+1 points)Located
alongside a cobblestoned street in Old City, Old City Photographics (OCP)
specializes in the processing of the traditional 35mm negative film, a once
dominant photographic medium now in decline due to the popularity of digital
photography. OCP offers three packages
to their customers. With the standard
package, the customer gets a set of 6×4 prints for $19.99. The deluxe package adds to the standard
package a CD-ROM of high resolution scans of the pictures for $29.99. Finally, the $39.99 pro package is similar to
the deluxe package in that it comes with a CD-ROM, although the customer gets a
contact print rather than a set of prints.
(A contact print is an 8×10 sheet of photographic paper that has all
pictures on the roll of film printed next to each other at reduced dimensions
and is used as an index.) The workflow
for OCP is shown below (s=standard, d=deluxe, p=pro): .jpg” alt=”OPC pfd”>OCP is operated by one person at every
station.(Part A) On average, OCP receive 13 jobs
per hour consisted of 44% standard, 37% deluxe and 19% pro. Which of the following statement best describes OCPs process? (3
Points)a.
The process is demand-constrained
(implied utilization is less than 1.0 at
all steps)b.
The process is
capacity-constrained and process film is the bottleneckc.
The process is
capacity-constrained and scan film is the bottleneckd.
The process is
capacity-constrained and make 6×4 prints is the bottleneck e. The process is capacity-constrained and make
contact print is the bottleneck(Part B) What is the implied utilization
(ratio of workload relative to capacity) at Scan Film (2 Points)a.
less than 50%b.
50% to 60%c.
60% to 70%d.
80% to 90%e.
90% to 100%f.
more than 100%Justify your answer:(Part C)
Fixing the relative proportions of job types, what is the largest number of
jobs per hour that OCP can handle?
Circle the answer closest to the correct answer. (2 Points)a.
10b.
11c.
12d.
14e.
16f.
18Justify your answer:question 4 – The right to vote (and not to wait) (6+1
points)In the previous
two presidential elections in the United States, very long wait times have been
witnessed at precincts (voting stations) in states that ultimately decided the
election (Florida in 2000 and Ohio in 2004). In Philadelphia as well, some voters
complained about the long lines in some precincts, with most complaints coming
from precinct A. In 2004, the average number of voters arriving at Precinct A
was of 35 per hour and the arrivals of voters was random with inter-arrival
times that had a coefficient of variation of 1 (CVa=1).Philadelphia had
deployed 1 voting machine in Precinct A. Suppose that each voter spent on
average 100 seconds in the voting booth (this is the time needed to cast
her/his vote using a voting machine), with a standard deviation of 120 seconds.(Part A) How
long on average a voter had to wait in line precinct at A in 2004 before entering in a booth to cast
her/his vote. Circle the closest answer. (3 Points)a.
56 minutesb.
58 minutesc.
60 minutesd.
62 minutese.
71 minutesf.
75 minutesg.
There is not sufficient information to answer
the questionJustify your answer:

Given the long
wait times for Precinct A, the city of Philadelphia is thinking of alternative
solutions to improve voting conditions. One of the proposed solutions is as
follows.Proposal 1:
Deploy an additional voting machine in precinct A. Assume that the voter
turnout is expected to have similar characteristics in 2008 as in the previous
election.(Part B) Under
Proposal 1, how long on average would a voter have to wait in line in precinct
A in 2008 before casting her/his vote. Circle the closest answer. (2 Points)a.
1 minuteb.
5 minutesc.
6 minutesd.
10 minutese.
11 minutesf.
There is not sufficient
information to answer the questionJustify your answer: (Part C) Under Proposal 1, on average,
at precinct A, what would be the ratio of the average number of people voting
(at a booth) over the average number of people in the line (waiting). Circle
the closest answer. (2 Points)a.
0.4b.
1.4c.
2.4d.
3.4 e.
4.4 f.
5.4 g.
There is not sufficient
information to answer the questionJustify your answer:question 5 – cranberries
again! (6+1 points)At OPLOG
Cranberry Cooperation (OCC!) cranberries arrive on truck at a rate of 150
barrels per hour. The inventory of OCC consists of three different levels. The
very first level can hold up to 200 barrels of cranberry. The second level can
hold up to 180 barrels of cranberry. The third level has unlimited
capacity. Assume the first level of
inventory is filled before the second level and
the second level is filled before the third level. The trucks
arrive uniformly from 6:00 AM to 2:00 PM. The OCC has three different groups of
workers. The first group start working at 6:30 AM and leave only if all the
inventory is processed. The first team of workers process cranberries at the
rate of 100 barrels per hour. The second group of workers join the first group
only if there are some cranberries left in the second level of inventory. Once
the second group join the first group, the cranberries will be processed at the
rate of 120 barrels per hour. The third group of workers join the second and
the first group only if they see some inventory in the third level. Once the
third group join the first two groups of workers, the cranberries are going to
be processed at the rate of 140 barrels per hour. (Part
A) What time will the second group of workers start
working? (1 Point) (Part
B) At what time(s) are there exactly 320 barrels of
cranberry in inventory ? (3 Points)(Part C) At
what time would OCC finish processing the cranberries. (3 Points)Bonus Question (1
point).manhattangmat.com/forums/how-many-zeros-does-100-end-with-t5008.html”>How many
zeros does 100! end with?