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