Attach computer work with the homework (add all printouts after the seventh problem).
1. Ace Advertising has won the contract to promote the Macaw Heads upcoming concert in
Aldrich. They have identified four relevant advertising outlets and using Nielson and Arbitron
data gathered the information in Table 1 about each advertising outlet. The advertising budget is
limited to $50,000. At least 500 thousand of the effective audience contact should be individuals
over the age of 40. For TV ads, the effective audience contact (and thus the percent of audience
over 40) drops by 20% after the 20th ad (include a decision variable for both maximum and
reduced effectiveness TV ad). The newspaper has agreed to cut the cost of an ad by 50% for
every additional ad purchased after the fifth ad. Thus the first five ads cost the regular price.
After the 6th regular price ad is purchased, the first reduced ad can be purchased. After the
seventh regular price ad is purchased, the second reduced ad can be purchased (include a
decision variable for the number of regular ads purchased and the number of reduced cost ads
purchase and be sure to require that the number of regular cost ads is always five more than the
reduced cost ads). At most, only 30 newspaper ads are possible. For every 106.7 radio ad, there
must be at least two 103.1 Radio ads. Formulate the LP model to determine the number of ads in
each outlet and maximize the effective audience contact.
.
Advertising
Outlets
Radio station 103.1
Radio station 106.7
Newspaper
TV
Effective Audience
Contact (000)
4
6
8
30
Percent of Effective
Audience over 40
80%
20%
60%
50%
Cost per ad
$200
$300
$400
$1000
1a). How many individuals over the age of 40 will be exposed to the ads? _________
1b). What would be the effective audience contact if the advertising budget was $60,000?
1c). More ads would be purchased for Radio station 106.7 if the effective audience contact was
equal to what value?
_____________
1d). How many newspaper ads should be purchased? _______________
2. Island Water Sports is a business that provides rental equipment and instruction for a variety
of water sports in a resort town. On one particular morning, a decision must be made of how
many Wildlife Raft Trips and how many Group Sailing Lessons should be scheduled. Each
Wildlife Raft Trip requires one captain and one crew person, and can accommodate six
passengers. The revenue per raft trip is $120. There are ten rafts available, and at least 30 people
are on the list for reservations this morning. Each Group Sailing Lesson requires one captain and
two crew people for instruction. Two boats are needed for each group. Four students will form
each group. There are 12 sailboats available, and at least 20 people are on the list for sailing
instruction this morning. The revenue per group sailing lesson is $160. The company has 12
captains and 18 crew available this morning. The company would like to maximize the number
of customers served while generating at least $1500 in revenue and honoring all reservations.
Formulate the LP model to determine how many Raft trips and how many Sailing lessons should
be scheduled.
2a, How many customers will be served? _________
2b. How may rafting trips should be scheduled? ____________
2c. What will be the total revenue? _________
2d. How many customers would be served if only 11 captains were available? _______
2e. It would only be beneficial to offer more sailing lessons if the number of customers per
sailing lesson was equal to what value?
_________ 3. A director for a summer camp recreation is
trying to choose activities for a rainy day. Information about possible choices is given in the table
below.
Category
Activity
Art
1. Painting
2. Drawing
Time
(minutes
)
30
20
3. Nature Craft
30
3
1
Music
4. Rhythm band
20
1
5
Sports
5. Relay races
45
4
1
6. Basketball
60
5
3
7. Internet
45
5
1
8. Creative writing
30
2
3
9. Games
40
5
2
Computer
Popularity
with
Campers
2
1
Popularity
with
Counselors
2
2
The popularity ratings are defined so that 5 is the most popular.
The objective is to keep the campers as happy as possible.
Formulate the integer LP model with the following conditions also apply:
a
At most one art activity can be done.
.
b
.
No more than two computer activities can be done.
c
.
If basketball is chosen, then the music must be chosen.
d
.
At least 120, but not more than 165 minutes of activities may be selected
e
.
To keep the staff happy, the counselor rating should sum of the chosen activities
should sum to at least 10.
3a. Which activities will be selected?
3b. What is the total popularity score with the campers for the chosen activities? _________
3c. What is the total popularity score with the counselors for the chosen activities? ________
d. How much time is required to complete all the chosen activities? _________
e. How many constraints are binding? ______
4. Phils Tennis Emporium Club has six indoor tennis courts. Phil is perplexed about how much
time to set aside during the clubs prime time hours this winter for each of the six revenue
producing activities listed in the table below. Prime time is from 5:00 PM to 10 PM Sunday
through Friday (i.e, each of the six courts is available for five hours per night, six nights per
week). To satisfy club members, Phil has decided that at least one-half of the available prime
time hours each week must be set aside for individual members play. A session for individual
members takes up one hour of court time and produces $10 revenue as shown in the table below.
League play has been an effective means of attracting new members to the club. Therefore, Phil
has scheduled four leagues for the winter term. Each league session requires four hours of court
time and generates $50 per session. Individual lessons by the head tennis pro, M. Hall, requires
one hour and generates $25 revenue, while individual lessons by the assistant pro, D. Martin,
requires one hour of court time and generates $20 revenue. M. Hall and D. Martin work together
during each group sessions (i.e., both are present during an adult group lesson and both are
present during a youth group lesson). Head pro M. Hall is only willing to work 30 hours per
week, while assistant pro D. Martin is willing to work up to 50 hours per week. Phil has decided
that youth group lessons are important for sustaining high membership in the future. Therefore,
Phil has decided that there must be at least five youth group sessions scheduled each week.
Formulate the integer LP model to determine how many sessions of each of the six activities
should be scheduled per week in order to maximize Phils weekly revenue.
Activity
Court hours per session
Individual member play
1 hour
League Play
4 hours
Individual Lesson (head pro)
1 hour
Individual Lesson (assistant pro)
1 hour
Group Lesson Adults
2 hours
Group Lesson Youth
2 hours
Revenue per session
$10
$50
$25
$20
$75
$40
4a. How many of each type of activity should be scheduled per week?
5. 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
MIN
Representatives
Professor Plum
Colonel Mustard
Ms Scarlett
Mrs. White
Miss Peacock
Mr. Green
The Butler
French Maid
CHI
6
2
7
8
8
7
7
8
6
4
7
4
6
4
5
7
Locations
BOS
N.O
LA
LV
MIA
4
1
3
7
8
5
3
2
4
5
1
6
2
6
5
1
3
4
5
6
3
4
1
2
3
7
2
5
1
8
6
5
3
8
1
2
2
5
8
1
7
3
3
1
4
2
8
6
Who should be assigned to each of the cities?
Representative
New York
_________________
Chicago
_________________
Boston
_________________
New Orleans
_________________
Los Angeles
_________________
Las Vegas
_________________
Miami
_________________
Minnesota
_________________
Total objective function value? __________________6 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
39
30
2
20
25
Table II
From
1
2
3
4
5
6
7
8
3
14
22
4
26
40
5
42
30
6
28
20
7
38
32
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
How many cars will be sent from and to each destination?
From
To
Number of Cars
________
________
_______
________
________
_______
________
________
_______
________
________
_______
________
________
_______
________
________
_______
7. Assume Acme Inc is considering introducing a new product - super Deluxe Widgets. The
Widgets will sell for $149 per unit. It is anticipated that the first year administrative costs will be
$50,000 and the first year advertising budget is projected to be $30,000. 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 $75 and a standard deviation of $15. 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 20,000 and 40,000. 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
$20
$25
$30
$35
$40
Probability
.20
.20
.35
.15
.10
7A). What is the mean profit on the 50 simulated trials?
7B) What is the standard deviation of the 50 simulated trials?
7C). How many simulated trials resulted in a loss?
7D). Of the 50 simulated trials, what was the maximum profit?