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Guest
Guest
I am not sure if this is in the right part of the forum or not, so please let it be moved if it needs to be. Now on to the problem, I have a word problem and i have to write out the constraints for the word problem. I have come up with the answer, but i am not sure if it is right or not. I wanted to see what other people can come up with, and then i will post what i have gotten for the answer. Here is the problem...
A large California-based consumer goods corporation has asked SALS Marketing Inc. to develop an advertising campaign for one of its new products. SALS has promised a plan that will yield the highest possible exposure rating, a measurement of the ability to reach the appropriate demographic group, which is correlated with demand produced per dollar spent on advertising. The media options (Magazines, Newspapers, Television, and Radio) for advertisements with their respective costs (per unit of advertising) and per unit exposure ratings are given in the Table 4.5. Of course, certain restrictions exist for the advertising campaign. The corporation has budgeted $800,000 for the campaign, but to restrict overexposure to any particular audience, wants no more than $300,000 put into any one of the four media alternatives. Also, to ensure a broad range of exposure, at least $100,000 must be spent in each medium. Develop an LP model for this situation.
Magazines-
Literary (cost/unit) $7,500 *** Exposure/unit 15,000
News (cost/Unit) $10,000 *** Exposure/Unit 22,500
Topical (Cost/unit) $15,000 *** Exposure/Unit 24,000
Newspapers--
Major Evening(Cost/Unit) $3,000 *** (Exposure/Unit) 75,000
Major Morning (Cost/Unit) $2,000 *** (Exposure/Unit 37,500
Television--
Morning (Cost/Unit) $20,000 *** Exposure/Unit 275,000
Mid-day (Cost/Unit) $10,000 *** Exposure/unit 180,000
Evening (Cost/Unit) $60,000 *** Exposure/Unit 810,000
Radio---
Morning (Cost/Unit) $15,000 *** 180,000
Mid-day (Cost/Unit) $15,000 *** 17,000
Evenining (Cost/Unit) $10,000 *** 16,000
PROBLEM # 2
Joe Dyer, the personnel manager of Racer, Inc., must schedule his security force in such a way to satisfy the staffing requirements shown below
Time Number of Officers Required
12:00 Midnight - 4 A.M. 5
4 A.M. - 8 A.M. 7
8 A.M. - 12:00 Noon 15
12:00 Noon - 4 P.M. 7
4 P.M. - 8 P.M. 12
8 P.M. - 12:00 Midnight 9
Officers may begin work at 12:00 Midnight, 4 A.M., 8 A.M., 12:00 Noon, 4 P.M., or 8 P.M. and work for 12-hour shifts. Mr. Dyer would like to minimize the total number of officers to employ each day. Furthermore, no more than 8 officers may begin their 12-hour shift at the same time. Develop an LP model for this problem.
A large California-based consumer goods corporation has asked SALS Marketing Inc. to develop an advertising campaign for one of its new products. SALS has promised a plan that will yield the highest possible exposure rating, a measurement of the ability to reach the appropriate demographic group, which is correlated with demand produced per dollar spent on advertising. The media options (Magazines, Newspapers, Television, and Radio) for advertisements with their respective costs (per unit of advertising) and per unit exposure ratings are given in the Table 4.5. Of course, certain restrictions exist for the advertising campaign. The corporation has budgeted $800,000 for the campaign, but to restrict overexposure to any particular audience, wants no more than $300,000 put into any one of the four media alternatives. Also, to ensure a broad range of exposure, at least $100,000 must be spent in each medium. Develop an LP model for this situation.
Magazines-
Literary (cost/unit) $7,500 *** Exposure/unit 15,000
News (cost/Unit) $10,000 *** Exposure/Unit 22,500
Topical (Cost/unit) $15,000 *** Exposure/Unit 24,000
Newspapers--
Major Evening(Cost/Unit) $3,000 *** (Exposure/Unit) 75,000
Major Morning (Cost/Unit) $2,000 *** (Exposure/Unit 37,500
Television--
Morning (Cost/Unit) $20,000 *** Exposure/Unit 275,000
Mid-day (Cost/Unit) $10,000 *** Exposure/unit 180,000
Evening (Cost/Unit) $60,000 *** Exposure/Unit 810,000
Radio---
Morning (Cost/Unit) $15,000 *** 180,000
Mid-day (Cost/Unit) $15,000 *** 17,000
Evenining (Cost/Unit) $10,000 *** 16,000
PROBLEM # 2
Joe Dyer, the personnel manager of Racer, Inc., must schedule his security force in such a way to satisfy the staffing requirements shown below
Time Number of Officers Required
12:00 Midnight - 4 A.M. 5
4 A.M. - 8 A.M. 7
8 A.M. - 12:00 Noon 15
12:00 Noon - 4 P.M. 7
4 P.M. - 8 P.M. 12
8 P.M. - 12:00 Midnight 9
Officers may begin work at 12:00 Midnight, 4 A.M., 8 A.M., 12:00 Noon, 4 P.M., or 8 P.M. and work for 12-hour shifts. Mr. Dyer would like to minimize the total number of officers to employ each day. Furthermore, no more than 8 officers may begin their 12-hour shift at the same time. Develop an LP model for this problem.
