Assignment.xlsx - Suppose the decision variables are as...

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Suppose the decision variables are as defined below: T1 = no. of Television advertisements with rating 90 and 4000 new customers T2 = no. of Television advertisements with rating 40 and 1500 new customers R1 = no. of radio advertisements with rating 25 and 2000 new customers R2 = no. of radio advertisements with rating 15 and 1200 new customers N1 = no. of newspaper advertisements with rating 10 and 1000 new customers N2 = no. of newspaper advertisements with rating 5 and 800 new customers Following is the Linear Programming Model we are using: Maximize 90T1+55T2+25R1+20R2+10N1+5N2 Subject to: 1) 1T1<10 2) 1R1<15 3) 1N1<20 4) 10000T1+10000T2+3000R1+3000R2+1000N1+1000N2<279000 5) 4000T1+1500T2+2000R1+1200R2+1000N1+800N2>100000 6) -2T1-2T2+1R1+1R2>0 7) 1T1+1T2<20 8) 10000T1+10000T2>140000 9) 3000R1+3000R2<99000 10) 1000N1+1000N2>30000 OPTIMAL SOLUTION is designed below: Objective Function Value = 2160.000 Variable Value Constraint Slack/Surplus T1 10 1 0.000 T2 5 2 0.000 R1 15 3 0.000 R2 18 4 0.000 N1 20 5 27100.000 N2 10 6 3.000 7 5.000 8 10000.000 9 0.000 10 0.000 OBJECTIVE COEFFICIENT RANGES ARE DESCRIBED IN THE BELOW MENTIONED TABLE: Variable Lower Limit Current Value Upper Limit
T1 55.000 90.000 No Upper Limit T2 No Lower Limit 55.000 66.667 R1 20.000 25.000 No Upper Limit R2 16.500 20.000 25.000 N1 5.000 10.000 No Upper Limit N2 No Lower Limit 5.000 5.500 Optimal Solution in summarized form is mentioned below: T1 + T2 = 15 Television advertisements R1 + R2 = 33 Radio advertisements N1 + N2 = 30 News Paper advertisements Advertising Schedule: Media Number of Ads Budget Television 15 150000 Radio 33 99000 News Paper 30 30000 Total 78 279000 Total Exposure Rating: 2,160 Total New Customers Reached: 127100 (Surplus constraint 5) 2. Solution: For each one dollar increase in the advertising budget the total exposure increa The analysis of Right Hand Side Ranges shows that this dual price applies for a b So this dual price applies to the $10,000 increase. So we can say that the Total Exposure Rating will increase by 10,000(0.006) = A $10,000 increase in the advertising budget is a 3.6% increase. But, it only prov This is a discussion topic for the management to decide that if the additional ex 3.Solution: For the first 10 television ads, the ranges for the exposure rating of 90 shows th So we can say the solution is not much depending upon the exposure rating HJ We can say that Flamingo is kind of inert to the exact exposure rating. The issue which needs to be concentrate on is the newspaper exposure rating o 4.Solution: We remove the constraint #5 for the linear programming model for developing
MAXIMIZE 4000T1+1500T2+2000R1+1200R2+1000N1+800N2 After solving the problem, following solution is obtained: T1 + T2 = 14 Television advertisements R1 + R2 = 28 Radio advertisements N1 + N2 = 55 New Paper advertisements Advertising Schedule: Media Number of Ads Budget Television 14 140000 Radio 28 83000 News Paper 55 55000 Total 97 278000 Total New Customers Reached: 139600 Total Exposure Rating = 2130 90(10) + 55(4) + 25(15) + 20(13) + 10(20) + 5(35) = 2130 5.Solution: The solution seems to be very effective. Following is the analysis : The total number of ads is increased from 78 to 97 (24%) and the number of po The preferred objective is to maximizing total exposure because this is consider message recall and appeal to repeat customers With this objective many new customers will be added keeping in mind the obje so the total exposure is reduced by 2160 – 2130 = 30 Now it depends upon the individual’s preference.

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