Question 1
The Denver advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $100,000 advertising budget ceiling placed on it. To do so, the agency needs to decide how much of the budget to spend on each of its two most effective media: (1) television spots during the afternoon hours and (2) large ads in the city?s Sunday newspaper. Each television spot costs $3,000; each Sunday newspaper ad costs $1,250. The expected exposure, based on industry ratings, is 35,000 viewers for each TV commercial and 20,000 readers for each newspaper advertisement. The agency director, Deborah Kellogg, knows from experience that it is important to use both media in order to reach the broadest spectrum of potential Breem customers. She decides that at least 5 but no more than 25 television spots should be ordered, and that at least 10 newspaper ads should be contracted. How many times should each of the two media be used to obtain maximum exposure while staying within the budget? Use the graphical method to solve.
For each of the above problems I need two things from you
(i) a formulation, and
(ii) solution using the graphical method. A formulation means putting the word problem into algebraic form. You must have defined decision variables, an objective function, and constraints.
Marketing
After production of goods or services, marketing is the next important step. This involves advertising, promotion, building relational and others to persuade people to purchase our goods or services. This function helps the company to reach to the end consumers.
Question 2
The Denver advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possbile for the product within the $100,000 advertising budget ceiling placed on it. To do so, the agency needs to decide how much of the budget to spend on each of its two most effective media:
(1) television spots during the afternoon hours and (2) large ads in the city’s Sunday newspaper. Each tv spot costs $3,000; each Sunday newspaper ad costs $1,250. The expected exposure, based on industry ratings, is 35,000 viewers for each TV commercial and 20,000 readers for each newspaper advertisement. The agency director, Deborah Kellogg, knows from experience that it is important to use both media in order to reach the broadest spectrum of potential Breem customers. She decides that at least 5 but no more than 25 TV spots should be ordered, and that at least 10 newspaper ads should be contracted.
How many times should each of the two media be used to obtain maximum exposure while staying within the budget? Use the graphical method to solve.
Question 3
The Denver advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $105 comma 000105,000 advertising budget ceiling placed on it. To do so, the agency needs to decide how much of the budget to spend on each of its two most effectivemedia: (1) television spots during the afternoon hours and (2) large ads in the city’s Sunday newspaper. Each television spot costs $3 comma 0003,000; each Sunday newspaper ad costs $1 comma 2501,250. The expected exposure, based on industry ratings, is 35 comma 00035,000 viewers for each TV commercial and 20 comma 00020,000 readers for each newspaper advertisement. The agencydirector, Deborah Kellogg, knows from experience that it is important to use both media in order to reach the broadest spectrum of potential Breem customers. She decides that at least 55 but no more than 2525 television spots should be ordered, and that at least 55 newspaper ads should be contracted. Aim of the objective function should be Maximize expected exposure. The optimum solution is: Number of TV spots = 55 (enter your response as a whole number). Number of newspaper advertisements = 7272 (enter your response as a whole number). Optimal solution value = 16150001615000 (enter your response as a whole number).
Answer to question 1
the number of television ads be t and number of newspaper ads be n,
Here, objective is to maximize exposure for the product;
This gives;
Optimal solution derive from the graph is (25,20) that means 25 television an 20 newspaper as will give maximum exposure of 1275000 people.
Answer to question 2
Let A = no. of TV spots
B = no. of newspaper advertisements
Objective function is to maximize the expected exposure
Z = MAX 35000 A + 20000B
Constraints:
3000 A + 1250 B <= 100000 (advertising Budget)
A >= 5 (at least 5 television spots)
A<= 25 (no more than 25 television spots)
B >= 10 (at least 10 newspaper ads should be contracted)
A, B >= 0 (Non negativity constraints)
Answer to question 3
Formulation:
Decision variables: Let T = Number of TV spots, N = Newspaper Ads
Objective: Max 35000T + 20000N
s.t.
3000T + 1250N <= 105000
T <= 25
T >= 5
N >= 5
T, N >= 0
Formulation and solution using Excel Solver is as follows
Formula used in above Excel spreadsheet model is D2 =SUMPRODUCT(B2:C2,$B$8:$C$8) this formula is copied to D2:D6
Optimal solution is: Number of TV sports = 5
Number of Newspaper Ads = 72
Optimal solution value = 1,615,000