The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and newspaper. Audienceestimates, costs, and maximum media usage limitations are as shown:ConstraintAudience per advertisementCost per advertisementMaximum media usageTo ensurebalanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.a. If the promotional budget is limited to $26080, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answerto nearest integer.T =Television Radio Newspaper120000 20000$1500 $21012 25Let T = number of television spot advertisementsR = number of radio advertisementsN = number of newspaper advertisementsR =N =37000$43010Budget $What is the total audience reached?b. By how much would audience contact increase if an extra $100 were allocated to the promotional budget?

Linear Programming is a mathematical modeling technique containing linear relationships that…

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Audience per advertisement Cost per advertisement Maximum media usage Television Radio Newspaper 120000 20000 $1500 $210 12 25 37000 $430 10

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Audience per advertisement Cost per advertisement Maximum media usage Television Radio Newspaper 120000 20000 $1500 $210 12 25 37000 $430 10

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter11: Linear Optimization Models

Section: Chapter Questions

Problem 9P: The Westchester Chamber of Commerce periodically sponsors public service seminars and programs....

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The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 100,000 16,000 35,000 Cost per advertisement $1,500 $250 $650 Maximum media usage 10 24 14 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $18,400, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0". No of commercial Advertisement Alternatives messages Television Radio Online What is the allocation of the budget…
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Radio Online Television Audience per advertisement Cost per advertisement Maximum media usage To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $15,900, how many commercial messages should be run on each medium to maximize total audience contact? Television Radio Budget (in dollars) Online Budget (in dollars) Total Audience Radio Online 300,000 54,000 120,000 $2,000 10 $300 20 $600 10 What is the allocation of the budget among the three…
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Television Radio Online Audience per advertisement 200,000 36,000 80,000 Cost per advertisement $2,000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $22,800, how many commercial messages should be run on each medium to maximize total audience contact? Television Radio 15 Online 10 What is the allocation of the budget among the three media, and what is the total audience reached? Television Budget (in…
Temax realtor company advertises for its business through television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 100000 18000 40000 Cost per advertisement 1800 300 600 Maximum media usage 12 18 12 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. 1. If the promotional budget is limited to $17600, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached? 2. By how much would audience contact increase if an extra $100 were allocated to the promotional budget
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached? By how much would audience contact increase if an extra $100 were allocated to the promotional budget?
A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided information on audience exposure, which the manager would like to maximize. After reviewing the research, the manager found the following linear optimization model for audience exposure, where x is the number of minutes of radio ads and y is the number of minutes of TV ads. Graph the constraints and identify the feasible region. Then identify each of the comer points and show how increasing the objective function value identifies the optimal solution. Maximize Exposure = 360x + 790y 400x+2000y ≤24,000 x-3y≤0 x≥0 and y≥0 Identify the graph of the feasible region. Choose the correct graph below. OA Ay 20- 10- 50' 100 OB. OC. Ay 20- Q 20 Q Q G 10- x 50 100 10- 50 100 Identify the vertices of the given feasible region. (Type an ordered pair, using integers or decimals rounded to two decimal places as needed. Use a comma to…
A linear programming computer package is needed. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Radio Audience per advertisement Online Cost per advertisement Maximum media usage Television Radio Budget Television Online Budget Total Audience 200,000 36,000 80,000 $2,000 Radio Online 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $20,500, how many commercial messages should be run on each medium to maximize total audience contact? $300 20 $600 What is the allocation of the budget…
A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided information on audience exposure, which the manager would like to maximize. After reviewing the research, the manager found the following linear optimization model for audience exposure, where x is the number of minutes of radio ads and y is the number of minutes of TV ads. Graph the constraints and identify the feasible region. Then identify each of the corner points and show how increasing the objective function value identifies the optimal solution. Maximize Exposure = 360x+790y 400x+2000y ≤24,000 x-3y ≤0 x20 and y 20 remory the graph of the feasible region. Chouse the corell graph below. OA Ay 20- OB. 10- G '50' 100 Identify the vertices of the given feasible region. 45 15 (0,0). (0,12) 2 2 Q Q 20- 20 20- 10- G '50' 100 50 100 10- G (Type an ordered pair, using integers or decimals rounded to two decimal places as…
The probabilities for the states of nature are P(8₁) = 0.20, P(82) = 0.30, and P(83) = 0.50 . For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant: P(F) = 0.69 P(U) = 0.31 P($1F) = 0.09 P(82|F) = 0.26 P(83| F) = 0.65 P($₁|U) = 0.45 P(82|U) = 0.39 P(83|U) = 0.16
The marketing department is considering a shift to internet-based advertising The advertising rates and demographics of several diflerent options are shown below. The marketing campaign goal is to reach the following audiences Age 18 to25−1,000,000inpressions Age 26 to35−1,500,000impressions Age 36 to45−750,000impressions What ino of advertising investment wat be most economical while stall meeting the gools? Note. Round your enswer to the nesrent whole number value.
The cost of introducing the products in selected geographic areas for gauging consumer response is $150K. If the company decides to introduce the product this way, it would need to see the responses to the products before they decide to launch the product line nationally. The probability of a favorable response in the selected geographical areas is estimated at O.60. La Comida can also decide not to go for the launching in the product in selected geographical areas and go ahead with the nationwide launch or not. If La Comida Foods decides to go full-blast in launching the products nationally and are a success, the company estimates that they will gain an annual income of $1.6 million. If the products are not a hit, the company will realize losses to the tune of $700K. La Comida estimates the probability of success for the sauces and marinades to be 0.50, if these are introduced without gauging consumer response.
The marketing department is considering a shift to internet-based advertising. The advertising rates and demographics of several different options are shown below. The marketing campaign goal is to reach the following audiences: Age 18 to 25 - 1,000,000 impressions Age 26 to 35- 1,500,000 impressions Age 36 to 45-750,000 impressions What mix of advertising investment will be most economical while still meeting the goals? Source A B Cost per thousand impressions (dollars) 30 20 Demographic breakdown 18-25 (30%), 26-35 (50%), 36-45 (20%) 18-25 (10 %), 26-35 (60%), 36-45 (30%) Note: Round your answer to the nearest whole number value. Investment in Source A (S) Investment in Source B ($)