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● on billboards and newspapers together must not exceed the amount spent on TV ads. While fund- raising is still continuing, the monthly budget for advertising has been set at $15,000. How many ads of each type should be placed to maximize the total number of people reached? 8-7 (Media selection problem) The advertising direc- tor for Diversey Paint and Supply, a chain of four retail stores on Chicago's North Side, is consider- ing two media possibilities. One plan is for a series of half-page ads in the Sunday Chicago Tribune newspaper, and the other is for advertising time on Chicago TV. The stores are expanding their lines of do-it-yourself tools, and the advertising director is interested in an exposure level of at least 40% within the city's neighborhoods and 60% in northwest sub- urban areas. The TV viewing time under consideration has an exposure rating per spot of 5% in city homes and 3% in the northwest suburbs. The Sunday newspaper has corresponding exposure rates of 4% and 3% per ad. The cost of a half-page Tribune advertisement is $925; a television spot costs $2,000. Diversey Paint would like to select the least costly advertising strategy that would meet desired exposure levels. (a) Formulate using LP. (b) Solve the problem. 8-8 (Automobile leasing problem) Sundown Rent-a- Car, a large automobile rental agency operating in the Midwest, is preparing a leasing strategy for the next six months. Sundown leases cars from an au- tomobile manufacturer and then rents them to the public on a daily basis. A forecast of the demand for Sundown's cars in the next six months follows: ONTH MARCH APRIL MAY JUNE JULY emand 420 400 430 460 470 AUGUST 440 Cars may be leased from the manufacturer for either three, four, or five months. These are leased on the first day of the month and are returned on the last day of the month. Every six months the automobile SEC

● on billboards and newspapers together must not exceed the amount spent on TV ads. While fund- raising is still continuing, the monthly budget for advertising has been set at $15,000. How many ads of each type should be placed to maximize the total number of people reached? 8-7 (Media selection problem) The advertising direc- tor for Diversey Paint and Supply, a chain of four retail stores on Chicago's North Side, is consider- ing two media possibilities. One plan is for a series of half-page ads in the Sunday Chicago Tribune newspaper, and the other is for advertising time on Chicago TV. The stores are expanding their lines of do-it-yourself tools, and the advertising director is interested in an exposure level of at least 40% within the city's neighborhoods and 60% in northwest sub- urban areas. The TV viewing time under consideration has an exposure rating per spot of 5% in city homes and 3% in the northwest suburbs. The Sunday newspaper has corresponding exposure rates of 4% and 3% per ad. The cost of a half-page Tribune advertisement is $925; a television spot costs $2,000. Diversey Paint would like to select the least costly advertising strategy that would meet desired exposure levels. (a) Formulate using LP. (b) Solve the problem. 8-8 (Automobile leasing problem) Sundown Rent-a- Car, a large automobile rental agency operating in the Midwest, is preparing a leasing strategy for the next six months. Sundown leases cars from an au- tomobile manufacturer and then rents them to the public on a daily basis. A forecast of the demand for Sundown's cars in the next six months follows: ONTH MARCH APRIL MAY JUNE JULY emand 420 400 430 460 470 AUGUST 440 Cars may be leased from the manufacturer for either three, four, or five months. These are leased on the first day of the month and are returned on the last day of the month. Every six months the automobile SEC

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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### Media Selection Problem **Context:** The advertising director for Diversey Paint and Supply, a chain of four retail stores on Chicago's North Side, is considering two media possibilities for expanding their do-it-yourself tools line. The goal is to achieve an exposure level of at least 40% within the city’s neighborhoods and 60% in northwest suburban areas. **Options:** 1. **Newspaper Ads:** - Medium: Sunday Chicago Tribune - Exposure Rates: 4% in city homes and 3% in northwest suburbs per ad. - Cost: $925 per half-page advertisement 2. **Television Ads:** - Medium: Chicago TV - Exposure Rates: 5% in city homes and 3% in northwest suburbs per spot. - Cost: $2,000 per spot **Objective:** To select the least costly advertising strategy that meets the desired exposure levels. **Tasks:** - (a) Formulate the problem using Linear Programming (LP). - (b) Solve the problem. ### Automobile Leasing Problem **Context:** Sundown Rent-a-Car, a large automobile rental agency in the Midwest, is developing a leasing strategy for the next six months. They lease cars from manufacturers to rent daily to the public. **Demand Forecast:** - March: 420 cars - April: 400 cars - May: 430 cars - June: 460 cars - July: 470 cars - August: 440 cars **Leasing Details:** - Cars can be leased from the manufacturer for three, four, or five months. - Leases start at the beginning of each month and end on the last day of the designated period. - The arrangement is part of their six-month planning cycle. The table below outlines the projected demand for Sundown's cars: | MONTH | MARCH | APRIL | MAY | JUNE | JULY | AUGUST | |--------|-------|-------|-----|------|------|--------| | Demand | 420 | 400 | 430 | 460 | 470 | 440 | Determine the optimal leasing strategy that meets these demands effectively.
Transcribed Image Text:### Media Selection Problem **Context:** The advertising director for Diversey Paint and Supply, a chain of four retail stores on Chicago's North Side, is considering two media possibilities for expanding their do-it-yourself tools line. The goal is to achieve an exposure level of at least 40% within the city’s neighborhoods and 60% in northwest suburban areas. **Options:** 1. **Newspaper Ads:** - Medium: Sunday Chicago Tribune - Exposure Rates: 4% in city homes and 3% in northwest suburbs per ad. - Cost: $925 per half-page advertisement 2. **Television Ads:** - Medium: Chicago TV - Exposure Rates: 5% in city homes and 3% in northwest suburbs per spot. - Cost: $2,000 per spot **Objective:** To select the least costly advertising strategy that meets the desired exposure levels. **Tasks:** - (a) Formulate the problem using Linear Programming (LP). - (b) Solve the problem. ### Automobile Leasing Problem **Context:** Sundown Rent-a-Car, a large automobile rental agency in the Midwest, is developing a leasing strategy for the next six months. They lease cars from manufacturers to rent daily to the public. **Demand Forecast:** - March: 420 cars - April: 400 cars - May: 430 cars - June: 460 cars - July: 470 cars - August: 440 cars **Leasing Details:** - Cars can be leased from the manufacturer for three, four, or five months. - Leases start at the beginning of each month and end on the last day of the designated period. - The arrangement is part of their six-month planning cycle. The table below outlines the projected demand for Sundown's cars: | MONTH | MARCH | APRIL | MAY | JUNE | JULY | AUGUST | |--------|-------|-------|-----|------|------|--------| | Demand | 420 | 400 | 430 | 460 | 470 | 440 | Determine the optimal leasing strategy that meets these demands effectively.
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