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. Cost per Ad $4550 $2860 $3910 $1875 Number of Customers Reached Medium TV Radio Magazines Internet 40000 17500 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. Decision variables here are to decide how many number of ads to put where within the given budget such that, we can reach maximum customers,
so, Number of TV adverts, Number of Radio,Number of Magazine, Number of internet adverts are the 4 decision variables
2.Objective here is to maximize the customers reached, if x,y,z and w are the above decision variables respectively, then the total number of customers reached is
40000x+17500y+18800z+10000w , we want to maximize this,
3.Given constraints are
total of magazine and radio adverts cannot be more than 15 i.e x+y<=15
number of internet should be atleast as many as number of TV adverts i.e w>=2x
total should be atleast 60 i,e x+y+z+w<=60
since the budget of advertisement is given 200000 i.e
4550*w+2860*x+3910*y+1875*z= 200000
Thumbs up if this was helpful, otherwise let me know in comments.

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