1. Homework Solution GOAL PROGRAMMING
SHAWHAN FILE WORKS
MGMT E-5050
Geraldine Shawhan is president of a firm that manufactures two
types of metal file cabinets.
Demand for her 2-drawer model is up to 600 weekly, while demand
for her 3-drawer model is limited to 400 weekly.
The firm has a weekly operating capacity of 1,300 hours, with the
2-drawer cabinet taking 1 hour to produce and the 3-drawer cabin-
et requiring 2 hours.
Each 2-drawer model yields a $10.00 profit, while the profit for the
large model is $

2. Homework Solution GOAL PROGRAMMING
SHAWHAN FILE WORKS
Shawhan has listed the following goals in order of importance:
Attain a profit as close to $11, as possible each week.
Avoid underutilization of the firm’s production capacity.
Sell as many 2-drawer cabinets and 3-drawer cabinets as
the demand indicates.
REQUIREMENT:
Formulate the goal programming model.
Solve this problem on QM for WINDOWS.

3. Homework Solution GOAL PROGRAMMING Let :
SHAWHAN FILE WORKS
Let :
X1 = number of 2-drawer cabinets produced weekly
X2 = number of 3-drawer cabinets produced weekly
d1 = underachievement of profit goal
d1 = overachievement of profit goal
d2 = idle time in production capacity
d3 = underachievement of sales goal for 2-drawer cabinets
d4 = underachievement of sales goal for 3-drawer cabinets - + - - -

4. Homework Solution GOAL PROGRAMMING - - - -+
Minimize deviations = P1d1 + P1d1 + P2d2 + P3d3 + P3d4
subject to : - +
10X1 + 15X2 + d1 – d1 = $11, ( profit target )
1X X2 + d2 - d2 = 1,300 hours ( production limit )
1X d3 - d3 = ( 2-drawer sales limit )
1X d4 - d4 = ( 3-drawer sales limit ) - + - + - +
All Xi , di variables => 0

5. Goal Programming with QM for WINDOWS
Shawhan File Works

8. 1st Goal, 1st Priority : Profit should be as close to $11,000
1st Goal, 1st Priority : Profit should be as close to $11,000. as possible
2nd Goal, 2nd Priority : Avoid underutilization of production capacity
3rd Goal, 3rd Priority : Sell as many 2-draw cabinets as demand states
3rd Goal, 3rd Priority : Sell as many 3-draw cabinets as demand states

9. 3

11. Priority 3
3rd

13. Homework Solution THE CAMPAIGN MANAGER GOAL PROGRAMMING
The campaign manager for a politician who is running for reelection
is currently engaged in the planning process. Four ways to advertise
have been selected: television ads, radio ads, billboards, and newspa-
per ads. The costs are as follows:
- $ for each television ad
- $ for each radio ad
- $ for a billboard for one month
- $ for each newspaper ad
The audience reached by each type of advertising has been estimated
at:
- 40,000 for each television ad
- 32,000 for each radio ad
- 34,000 for each billboard
- 17,000 for each newspaper ad
The total monthly advertising budget is $16,000.00

14. THE CAMPAIGN MANAGER
Homework Solution
The following goals have been established and ranked:
The number of people reached should be at least 1,500,000.
The total monthly advertising budget should not be exceeded.
Together, the number of ads on either television or radio should
be at least six (6).
No more than ten (10) ads of any type of advertising should be
used.
REQUIREMENT:
Formulate this as a goal programming problem.
Solve this problem via QM for WINDOWS.
Which goals are completely met and which of them are not?

15. Homework Solution GOAL PROGRAMMING
THE CAMPAIGN MANAGER
Homework Solution
GOAL PROGRAMMING
Let : X1 = the number of television ads
X2 = the number of radio ads
X3 = the number of billboard ads
X4 = the number of newspaper ads
Subject to :
(1) the number of people reached.
(2) the budget.
(3) the number of TV or radio ads.
(4) restriction on the number of each
individual type of ad.

16. THE CAMPAIGN MANAGER
Homework Solution
Minimize deviations = P1d1- + P2d2+ + P3d3- + P4d4+ + P4d5+ P4d6+ + P4d7+
subject to :
The number of people reached:
40,000 X1 + 32,000 X2 + 34,000 X3 + 17,000 X4 –d1+ + d1- = 1,500,000
The budget:
900 X X X X4 –d2+ + d2- = 16,000
The number of television or radio ads:
X1 + X2 –d3+ + d3- = 6
Restriction on the number of each individual type of ad:
X1 – d4+ + d4- = X3 –d6+ + d6- = 10
X2 – d5+ + d5- = X4 –d7+ + d7- = 10
X1 , X2 , X3, X4 , and all di => 0 non-negativity constraint

17. Homework Solution SUMMARY The number of television ads = 0
THE CAMPAIGN MANAGER
Homework Solution
SUMMARY
The number of television ads = 0
The number of radio ads = .73 ≈ 0
The number of billboard ads = 0
The number of newspaper ads = 88.86
The number of newspaper ads was exceeded by 78.86
Goal #1 – the number of people reached was met exactly.
Goal #2 – the budget of $16, was met ($15,994.80)
Goals #3 and #4 – not met ; the number of television, radio,
and billboard ads are each less than 10.

18. Goal Programming with QM for WINDOWS
The Campaign Manager

20. 3

21. 3

22. 3

23. 3

24. 88.86 newspaper ads @ $180.00 = $15,994.80 88.86 newspaper ads3
88.86 newspaper ads
@ 17,000 people
reached
= 1,510,620 people
Audience exposure
and budget are met
completely.
The number of TV,
radio, and billboard
ads are each less than
10.
The other goals are
not met.