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1. Acme Inc must send a representative to each of eight different satellite locations. Eight Acme representatives have been identified for the assignments. One representative will be sent to each of the eight satellite locations. In order to make the assignments each representative has been asked to rank their preferences from 1 – most favorable assignment to 8 – their least favorable assignment. The rankings appear in the table below. Determine which representative should be sent to each location in order to minimize the rankings and avoid sending representatives to the least favorable locations. Turn in computer printout along the answers

Locations
NYC CHI BOS N.O LA LV MIA MIN
Representatives
Professor Plum 3 4 6 1 7 8 5 2
Colonel Mustard 2 3 7 4 5 1 6 8
Ms Scarlett 2 8 6 5 1 3 4 7
Mrs. White 7 5 6 3 4 1 2 8
Miss Peacock 1 3 7 2 5 6 8 4
Mr. Green 7 6 5 3 8 1 2 4
The Butler 1 2 5 8 6 7 3 4
French Maid 5 3 4 1 2 8 6 7




2 Frugal Rent-A-Car has eight store lots in the Greater St. Louis Metropolitan area. At the beginning of each day, they would like to have a predetermined number of cars available at each lot. However, since customers renting a car may return the car to any of the eight lots, the number of cars available at the end of the day does not always equal the designated number of cars needed at the beginning of the day. Frugal would like to redistribute the cars in the lots to meet the minimum demand and minimize the time needed to move the cars.
Table I below, summarizes the results at the end of one particular day.
Table II below summarizes the time required to travel between the lots.
Solve the problem in order to determine how many cars should be transported from one lot to the next. Turn in computer printout along the answers
Table I Lot
Cars 1 2 3 4 5 6 7 8
Available 37 20 14 26 40 28 38 52
Desired 30 25 20 40 30 20 30 60

Table II To (in minutes)
From 1 2 3 4 5 6 7 8
1 -- 12 17 18 10 20 40 35
2 14 -- 10 19 16 15 28 32
3 14 10 -- 12 8 9 34 26
4 8 16 14 -- 12 15 44 38
5 11 21 16 18 -- 10 24 28
6 24 12 9 17 15 -- 36 35
7 38 30 32 40 25 38 -- 29
8 30 34 28 35 31 33 31 --



3. Minus Mufflers provides three types of automobile service for their customers – (1) extraneous muffler replacements, (2) bogus radiator repairs, and (3) unnecessary brake-pad replacements. Three of Minus’s employees do all the work. Mr. Henry is the only employee customers are allowed to talk to. Mr. Henry’s job includes, greeting the customers, explaining what is wrong with their car, the total costs involved and handling the paper work. A second employee, A. Capone is the inspector. A. Capone is responsible for examining the cars when they arrive at Minus and finding something wrong with the car. The third employee, Max, does all the repair work. The time required by each employee for each repair and the maximum number of hours each employee is willing to work per week is given in the table below. Minus ads guarantee their mufflers for the lifetime of the car. Therefore to avoid having to replace a muffler for free, Minus never installs their own brand, but rather installs A-1 mufflers. Minus has a contract to receive up to 40 A-1 mufflers per week (thus a maximum on only 40 muffler repairs can be performed each week). In addition, A Capone believes that at least 30% of the repairs should be radiator repairs. For kickback purposes, Mr. Haney requires that no more than 50% of repairs involve brake pad replacements. Finally, Max is unwilling to spend more than half of his actual working time (not the Maximum number of hours worked) performing radiator repairs. Formulate the LP model to maximize weekly profit and determine how many repairs of each time should be conducted per week.

Mr. Haney A.Capone Max
Service Profit time/repair time/repair time/repair
Muffler $70 15 minutes 10 minutes 30 minutes
Radiator $180 30 minutes 15 minutes 60 minutes
Brakes $95 15 minutes 15 minutes 20 minutes

Max hours/week 35 hours 25 hours 65 hours




4. G and P Manufacturing would like to minimize the labor cost of producing dishwasher motors for a major appliance manufacturer. Although two models of motors exist, the finished models are indistinguishable from one another; their cost difference is due to a different production sequence. The time in hours required for each model in each production area is tabled below along with the labor cost.

Model 1 Model 2
Area A 15 6
Area B 4 8
Area C 4 8
Revenue 90 65

Currently labor assignments provide for 10,000 hours in each of Areas A and B and 18000 hours in Area C. In addition, it is possible to transfer 2000 hours from area B to Area A. Similarly, 3000 hours may be transferred from area C to either Areas A or B. Develop the linear programming model to indicate how many of each model should be produced and how to allocate the workforce in order to maximize revenue.


5 Springmeadow Park Board is considering a new recreation complex with a variety of facilities. Expected costs (in thousands), space requirement (in square feet), and projected average usage figures are given in the table below. The department has a total of $1 million to spend specifically for the facilities. The building will have a maximum size of 20,000 square feet allocated to the indoor facilities listed below (thus this area excludes offices, lobbies, meeting rooms, etc.). In addition, there will be a maximum of 50,000 square feet of outdoor space available for these facilities. Councilman Bundy feels strongly that at most only one pool should be included in the complex. Councilwoman Simpson, whose daughter skates and son plays soccer, insists that if a baseball field is built then both a skating rink and soccer field must also be included in the park. If the park board wishes to maximize average usage of the complex, formulate the integer programming problem to determine which facilities should be included.

Facility Cost Space requirements Expected usage/day
Fitness Center (I) $200 2,000 60
Pool (I) 80 5,500 75
Pool (O) 65 7,200 40
Auditorium (I) 150 5,000 30
Gymnasium (I) 250 7,500 60
Tennis courts (O) 60 5,000 15
Baseball field (O) 90 25,000 35
Soccer fields (O) 80 25,000 44
Skating rink (I) 250 5,000 25

(I) indoor (O) outdoor



6. Assume Acme Inc is considering introducing a new product - super Deluxe Widgets. The Widgets will sell for $229 per unit. It is anticipated that the first year administrative costs will be $10,000 and the first year advertising budget is projected to be $8,000. The direct labor costs are uncertain, but it is believed they can be accurately can be represented by a normal distribution with a mean of $90 and a standard deviation of $30. Experts in the area have subjectively estimated the parts cost can be simulated by the discrete probability distribution listed below. The forecasted demand for the first year may be represented by a uniform distribution with limits of 500 and 700. Obtain summary statistics for 50 simulated trials to answer the four questions listed below. (Turn in the computer printout along with this answer sheet).

Cost per unit Probability
$60 .20
$65 .25
$70 .30
$75 .15
$80 .10
QBA HW.docx

1. Acme Inc must send a representative to each of eight different satellite locations. Eight
Acme representatives have been identified for the assignments. One representative will
be sent to each of the eight satellite locations. In order to make the assignments each
representative has been asked to rank their preferences from 1 most favorable
assignment to 8 their least favorable assignment. The rankings appear in the table
below. Determine which representative should be sent to each location in order to
minimize the rankings and avoid sending representatives to the least favorable locations.
Turn in computer printout along the answers
NYC
MIA
Representatives
Professor Plum
Colonel Mustard
Ms Scarlett
Mrs. White
Miss Peacock
Mr. Green
The Butler
French Maid

Locations
CHI
BOS
MIN

3
5
2
6
2
4
7
2
1
8
7
2
1
3
5
6

4
2
3
8
8
7
5
8
3
4
6
4
2
4
3
7

N.O

LA

LV

6

1

7

8

7

4

5

1

6

5

1

3

6

3

4

1

7

2

5

6

5

3

8

1

5

8

6

7

4

1

2

8

2 Frugal Rent-A-Car has eight store lots in the Greater St. Louis Metropolitan area. At the
beginning of each day, they would like to have a predetermined number of cars available at each
lot. However, since customers renting a car may return the car to any of the eight lots, the
number of cars available at the end of the day does not always equal the designated number of
cars needed at the beginning of the day. Frugal would like to redistribute the cars in the lots to
meet the minimum demand and minimize the time needed to move the cars.
Table I below, summarizes the results at the end of one particular day.
Table II below summarizes the time required to travel between the lots.
Solve the problem in order to determine how many cars should be transported from one
lot to the next. Turn in computer printout along the answers

Table I
Cars
Available
Desired

Lot
1
37
30

2
20
25

Table II
From
1
2
3
4
5
6
7
8

3
14
20

4
26
40

5
40
30

6
28
20

7
38
30

8
52
60

6
20
15
9
15
10
-38
33

7
40
28
34
44
24
36
-31

8
35
32
26
38
28
35
29
--

To (in minutes)
1
-14
14
8
11
24
38
30

2
12
-10
16
21
12
30
34

3
17
10
-14
16
9
32
28

4
18
19
12
-18
17
40
35

5
10
16
8
12
-15
25
31

3. Minus Mufflers provides three types of automobile service for their customers (1)
extraneous muffler replacements, (2) bogus radiator repairs, and (3) unnecessary brakepad replacements. Three of Minuss employees do all the work. Mr. Henry is the only
employee customers are allowed to talk to. Mr. Henrys job includes, greeting the
customers, explaining what is wrong with their car, the total costs involved and handling
the paper work. A second employee, A. Capone is the inspector. A. Capone is
responsible for examining the cars when they arrive at Minus and finding something
wrong with the car. The third employee, Max, does all the repair work. The time
required by each employee for each repair and the maximum number of hours each
employee is willing to work per week is given in the table below. Minus ads guarantee
their mufflers for the lifetime of the car. Therefore to avoid having to replace a muffler
for free, Minus never installs their own brand, but rather installs A-1 mufflers. Minus has
a contract to receive up to 40 A-1 mufflers per week (thus a maximum on only 40 muffler
repairs can be performed each week). In addition, A Capone believes that at least 30% of
the repairs should be radiator repairs. For kickback purposes, Mr. Haney requires that no
more than 50% of repairs involve brake pad replacements. Finally, Max is unwilling to
spend more than half of his actual working time (not the Maximum number of hours
worked) performing radiator repairs. Formulate the LP model to maximize weekly profit
and determine how many repairs of each time should be conducted per week.
Service
Muffler
Radiator
Brakes

Profit
$70
$180
$95

Mr. Haney
time/repair
15 minutes
30 minutes
15 minutes

A.Capone
time/repair
10 minutes
15 minutes
15 minutes

Max
time/repair
30 minutes
60 minutes
20 minutes

Max hours/week

35 hours

25 hours

65 hours

4. G and P Manufacturing would like to minimize the labor cost of producing
dishwasher motors for a major appliance manufacturer. Although two models of motors
exist, the finished models are indistinguishable from one another; their cost difference is
due to a different production sequence. The time in hours required for each model in each
production area is tabled below along with the labor cost.
Area A
Area B
Area C
Revenue

Model 1
15
4
4
90

Model 2
6
8
8
65

Currently labor assignments provide for 10,000 hours in each of Areas A and B and
18000 hours in Area C. In addition, it is possible to transfer 2000 hours from area B to
Area A. Similarly, 3000 hours may be transferred from area C to either Areas A or B.
Develop the linear programming model to indicate how many of each model should be
produced and how to allocate the workforce in order to maximize revenue.
5 Springmeadow Park Board is considering a new recreation complex with a variety of
facilities. Expected costs (in thousands), space requirement (in square feet), and
projected average usage figures are given in the table below. The department has a total
of $1 million to spend specifically for the facilities. The building will have a maximum
size of 20,000 square feet allocated to the indoor facilities listed below (thus this area
excludes offices, lobbies, meeting rooms, etc.). In addition, there will be a maximum of
50,000 square feet of outdoor space available for these facilities. Councilman Bundy
feels strongly that at most only one pool should be included in the complex.
Councilwoman Simpson, whose daughter skates and son plays soccer, insists that if a
baseball field is built then both a skating rink and soccer field must also be included in
the park. If the park board wishes to maximize average usage of the complex, formulate
the integer programming problem to determine which facilities should be included.
Facility
Fitness Center (I)
Pool (I)
Pool (O)
Auditorium (I)
Gymnasium (I)
Tennis courts (O)
Baseball field (O)

Cost
$200
80
65
150
250
60
90

Space requirements Expected usage/day
2,000
60
5,500
75
7,200
40
5,000
30
7,500
60
5,000
15
25,000
35

Soccer fields (O)
Skating rink (I)

80
250

25,000
5,000

44
25

(I) indoor (O) outdoor

6. Assume Acme Inc is considering introducing a new product - super Deluxe Widgets.
The Widgets will sell for $229 per unit. It is anticipated that the first year administrative
costs will be $10,000 and the first year advertising budget is projected to be $8,000. The
direct labor costs are uncertain, but it is believed they can be accurately can be
represented by a normal distribution with a mean of $90 and a standard deviation of $30.
Experts in the area have subjectively estimated the parts cost can be simulated by the
discrete probability distribution listed below. The forecasted demand for the first year
may be represented by a uniform distribution with limits of 500 and 700. Obtain
summary statistics for 50 simulated trials to answer the four questions listed below.
(Turn in the computer printout along with this answer sheet).
Cost per unit
$60
$65
$70
$75
$80

Probability
.20
.25
.30
.15
.10

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