Question

In: Statistics and Probability

FIRMCo is planning an advertising campaign, budgeted at $70000. Each 1000 dollars spent on radio ads,...

  1. FIRMCo is planning an advertising campaign, budgeted at $70000. Each 1000 dollars spent on radio ads, results in 70 new customers. Similarly, each 1000 dollars spent on TV ads yield 105 new customers. Each radio ad costs $250, and each TV ad costs $1500. The combined number of ads used in the campaign cannot exceed 75. The amount spent on radio ads, and the amount spent on TV ads cannot differ from one another by more than $15000. Define the two decision variables by R and TV (the amount in thousand dollars, spent on radio ads and TV ads. For example, if R=7 then 7000 is spent on radio ads. Answer the following questions about the linear programming model that maximizes the number of new customers.

2.1 The objective function is:

  1. Max (1000*R)/70 + (1000*TV)/105
  2. Max 70R + 105*TV
  3. Max (70+105)*1000*(R+TV)

2.2 The budget constraint is:

a. R + TV <= 70000

b. R/1000 + TV/1000 <= 70

c. R + TV <= 70

2.3 The constraint on the combined number of ads is:
      a. (R*250 + TV*1500)/70 >= 75

      b. 1000R/250 + 1000TV/1500 <= 75
      c. R/250 + TV/1500 <=70000/75

      d. (R+TV)/(250+1500) <=75

2.4 The constraint (or constraints) on the amounts spent on the two media is:

      a. We need two constraints: R – TV <= 15, and TV – R <= 15.

      b. We can either use R – TV <= 15, or TV – R <= 15, but not both.

      c. We need two constraints: R <= 15 and TV >= 15.

d. R – TV >= 15, and TV – R >= 15

Solutions

Expert Solution


Related Solutions

Top Toys is planning a new radio and TV advertising campaign. A radio commerical costs $300...
Top Toys is planning a new radio and TV advertising campaign. A radio commerical costs $300 and a TV ad costs $2000. A total budget of $20,000 is allocated to the campaign. However, to ensure that each medium will have at least one radio commercial and one TV ad, the most that can be allocated to either medium cannot exceed 80% of the total budget. It is estimated that the first radio commerical will reach 5000 people, with each additional...
To compare the effectiveness of a media campaign - via radio ads, billboards, and ads on...
To compare the effectiveness of a media campaign - via radio ads, billboards, and ads on social media websites - to reduce the incidence of impaired driving, a police chief inspected data from 60 randomly chosen CheckStops at varying locations.Thirty of these were before the launch of this campaign, 30 were after the media campaign had been running for a months time. Use α=0.05α=0.05 for all calculations. For each CheckStop randomly chosen, the number of people charged with impaired driving...
A hardware store will run an advertising campaign using radio and newspaper. Every dollar spent on...
A hardware store will run an advertising campaign using radio and newspaper. Every dollar spent on radio advertising will reach 60 people in the "Under $35,000" market, and 60 people in the "Over $35,000" market. Every dollar spent on newspaper advertising will reach 100 people in the "Under $35,000" market, and 20 people in the "Over $35,000" market. If the store wants to reach at least 210,000 people in the "Under $35,000" market and 240,000 people in the "Over $35,000"...
A department store is planning their Spring advertising campaign. They have budgeted $200,000 to use for...
A department store is planning their Spring advertising campaign. They have budgeted $200,000 to use for advertising, and wish to reach the maximum number of potential customers. The advertising firm they are using has carefully obtained the following planning data, to ensure that their client is able to get the most customer impressions possible. Characteristics Advertising Medium Newspaper Radio Television People reached per unit 40,000 120,000 175,000 Number of persons with higher income per unit 25,000 40,000 56,000 Number of...
Acme Advertising has a $10,000 budget for a combination of television ads ($300 each) and radio...
Acme Advertising has a $10,000 budget for a combination of television ads ($300 each) and radio ads ($125 each) for a new client (a sporting goods store) and wants to maximize total reach. Television ads reach 5,000 people while radio ads reach 3,500 people. The television ads are to be run during local college basketball games with the goal of running at least 5 ads and no more than 20 ads. Radio ads will be run at the same time...
Two advertising media are being considered for promotion of a product. Radio ads cost $400 each,...
Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while Newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type. Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people. The company wishes to maximize the number of people that are reached while meeting all the constraints stated. Write the LP...
Ads: A company is willing to renew it advertising contact with a local radio station only...
Ads: A company is willing to renew it advertising contact with a local radio station only if the station can prove that more than 20% of the residents of the city heard the ad and not recognize the company’s product. The radio station conducts a random phone survey of 400 people. A) What are the hypotheses B) The station plans to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%?...
An advertiser who is planning a radio campaign is interested in the number of minutes of...
An advertiser who is planning a radio campaign is interested in the number of minutes of music played per hour by five local radio stations. A sample of 4 hours is taken from each station. Complete the following analysis, using the information given, and using a 0.05 level of significance. For full marks your answer should be accurate to at least two decimal places. Sample means FM 92 FM 97 FM 101 FM 104 FM 107 50 46.5 53.25 48.5...
An advertiser who is planning a radio campaign is interested in the number of minutes of...
An advertiser who is planning a radio campaign is interested in the number of minutes of music played per hour by five local radio stations. A sample of 5 hours is taken from each station. Complete the following analysis, using the information given, and using a 0.05 level of significance. For full marks your answer should be accurate to at least two decimal places. Sample means FM 92 FM 97 FM 101 FM 104 FM 107 50.6 51.4 44.6 48.8...
Ads A company is willing to renew its advertising contract with a local radio station only...
Ads A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product. The radio station conducts a random phone survey of 400 people. a. What are the hypotheses? b. The station plans to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT