5. An advertising campaign for a new product will be conducted in Baltimore area

Question

5. An advertising campaign for a new product will be conducted in Baltimore area and can use TV, radio, magazines, and internet advertisements. Information about each medium is shown below. Number of Customers Reached Medium TV Radio Magazines Internet Cost per Ad $4550 $2860 $3910 $1875 40000 7500 18800 10000 The total number of magazines advertisements and the number of radio advertisements cannot be more than 15. The number of internet advertisements should be at least as many as the number of advertisements on TV There must be at least a total of 60 advertisements in all four media. The advertising budget is $200,000.The objective is to maximize the total number of customers reached. (a) Define the decision variables. (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem after formulating

Explanation / Answer

Hi,
1. since the choice to make here is to decide the distribution of advertisements such that number of customers are maximized, the decision variables are
No of Tv adverts- let it be a
No of Radio adverts- let it be b
No of Magazine adverts- let it be c
No of Internet adverts- let it be d
2.The objective here is to maximize the customers reached, so lets write a formula to get the number of customers
since given customers for each type of advertisement, we have
40000 *a +17500*b+18800*c+10000 *d
3. lets formulate the constraints now,
total no of magazine and radio advertisements cannot be more than 15 i.e a+b<=15
number of internet advertisements should be atleast as many as number of TV i.e d>=2*a
total of advertisements should be min 60 i.e a+b+c+d<=60
the budget of advertisement is 200000 i.e
4550*a+2860*b+3910*c+1875*d= 200000

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