Goal Programming The Relax-and-Enjoy Lake Development Corporation is developing a lakeside community at a privately

Goal Programming
The Relax-and-Enjoy Lake
Development Corporation is developing a lakeside community at a privately
owned lake and is in the business of selling property for vacation and/or
retreat cottages. The primary
market for these lakeside lots includes all middle and upper income
families within approximately 100 miles of the development. Relax-and-Enjoy has employed the
advertising firm of Boone, Phillips and Jackson to design the promotional
campaign for the project.
After considering possible
advertising media and the market to be covered,

Boone has made the preliminary
recommendation to restrict the first month’s
advertising to five sources. At the end of this month, Boone will then
reevaluate
its strategy based upon the month’s
results. Boone has collected data on a
number
of potential purchase families reached,
the cost per advertisement, the maximum
number of times each medium is available,
the expected exposure for each of the
five media. The expected exposure is measured in terms of
an exposure unit, a
management judgment measure of the
relative value of one advertisement in each
of the media. The measures based on Boone’s experience in
the advertising
business take into account such factors as
audience profile (age, income, and
education of the audience reached), image
presented, and quality of the
advertisement. The information collected to date is
presented below.
Advertising
Media Alternatives for the
Relax-and-Enjoy
Lake Development Corporation
Number
of

Potential
Maximum
Purchase Cost per Times Expected
Families Advertise- Available Exposure
Advertising Media Reached ment per Month* Units
1. Daytime TV (1
min) 1000 $1500 15 65
Station WKLA
2. Evening TV
(30s) 2000 $3000 10 90
Station WKLA
3. Daily
newspaper 1500 $400 25 40
(full page), The
Morning Journal
4. Sunday
newspaper 2500 $1000 4 60
Magazine (1/2 pg.
Color). The Sunday
Press.
5. Radio, 8:00 a.m. or 300 $100 30 20
5:00 p.m. news (30’s)
__Station KNOP_________________________________________________________
*The maximum number of times the medium is available is
either the maximum number of times the advertising medium occurs (e.g. four
Sundays for medium 4) or the maximum number of times Boone will allow the
medium to be used.
Relax-and-Enjoy
has provided Boone with an advertising budget of $30,000 for the first month’s
campaign. In addition Relax-and-Enjoy
has the following goals and priorities regarding how Boone allocates these
funds, as follows:
Goal
1: To utilize at least 10 television
commercials (Priority 1).
Goal
2: To reach at least 50,000 potential
purchases during the month

(Priority 2).
Goal 3:
To spend no more than $18,000 on television advertisements

(Priority 3).
Goal
4: To come as close as possible to
achieving 2400 exposure units

(Priority 4).
Goal
5: To minimize the advertising budget
(Priority 5).
(a) Formulate
a goal programming model of this problem:
DTV= Daytime TV, ETV= Evening TV,
DNP= Daily Newspaper, SNP= Sunday Newspaper, R= Radio
Economic constraints:
Goal constraints:
Objective function:
(b) Suppose
that Boone is working on a similar but smaller problem for
another client, and they are considering
only two media alternatives,
evening T.V. and the daily
newspaper. This second problem can be
modified as follows:
3000 X1 + 400 X2
= $24,000 Budget
X1 – d1+
+ d1- = 7
X2 – d2+
+ d2- = 15
2000 X1 + 1500 X2
– d3+ + d3- = 30,000
Min Z= P1d1-
+ P2 d2++ P3d3-
+ P4 (-d1+)

Determine the optimal solution
for this problem. Give the values of all
variables.