Question

1. MEDIA SELECTION PROBLEM: The TTK Company has recently developed a new karaoke machine, and has $150,000 to spend on advertising. The product is to be initially test marketed in the Philadelphia area. The money is to be spent on a TV advertising blitz during one weekend (consisting of Saturday and Sunday) in April. There are three options available on both Saturday and Sunday: morning advertising, afternoon advertising and evening news advertising. A mixture of oneminute TV spots is desired. The goal of the campaign is to maximize the total audience reached, while staying within budget.

Ad Type Estimated Audience Reached Cost per Ad

Morning Ad 3000 $4000

Afternoon Ad 500 $800

Evening Ad 5000 $6000

TTK wants to take out at least one ad of each type (morning, afternoon, and evening). There are ten daytime (= morning and afternoon) spots available on both Saturday and Sunday. There are four evening spots available on Saturday. Further, there are only three Sunday evening ad spots available. TTK wants to have at least 3 ads per day, but spend no more than $70,000 on Saturday and no more than $100,000 on Sunday. Define the following decision variables for the problem and answer the questions based upon this information:

MSA = number of morning ads on Saturday

ASA = number of afternoon ads on Saturday

ESA = number of evening ads on Saturday

MSU = number of morning ads on Sunday

ASU = number of afternoon ads on Sunday

ESU = number of evening ads on Sunday

Answer 1

Decision variables :

Number of ads of type Morning,Afternoon and Evening to be taken on Saturday and Sunday.

Objective function :

Maximum Audience Reached =H11=SUMPRODUCT(C10:C12,C3:C5)+SUMPRODUCT(D10:D12,C3:C5)=60000

Constraints :

C15=C10

C16=C11

C17=C12

C18=D10

C19=D11

C20=D12

C21=SUM(C10:D11)

C22=C12

C23=D12

C24=SUM(C10:C12)

C25=SUM(D10:D12)

C26=SUMPRODUCT(C10:C12,D3:D5)

C27=SUMPRODUCT(D10:D12,D3:D5)

The optimal solution is as shown below :

MSA=1

ASA=1

ESA=4

MSU=7

ASU=1

ESU=3