# 2 objective function to maximize the customer reached

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2. Objective Function: – To maximize the customer reached across all media. Max 4000 T1 + 1500 T2 +2000 R1 + 1200 R2 + 1000 O1 + 800 O1 3. Constraints: 10000T1 + 10000T2 +3000R1 + 3000R2 + 1000 O1 + 1000 O2 <=279000 (Total Budget) 4000 T1 + 1500 T2 +2000 R1 + 1200 R2 + 1000 O1 + 800 O1 >= 100000 (Customer Reach) R1+ R2 -2T1 -2T2 >= 0 (Radio advertisement Lower bound) T1 + T2 <= 20 (TV Advertisements Upper bound) 10000 T1 + 10000 T2 >= 140000 (TV budget Lower bound) 3000 R1 + 3000 R2 <= 99000 (Radio Budget Upper bound) 1000 O1 + 1000 O2 >= 30000 (Online budget Lower bound) T1 <=10 (Television first 10 ads) R1 <=15 (Radio first 15 ads) O1 <=20 (Online first 20 ads) T1, T2, R1, R2, O1, O2 >= 0 (Non-Negative) 2
LP Solution Model 1 Maximizing Exposure Rating Max Exposure rate = 2160, when T1 =10, T2 = 5, R1 = 15, R2 = 18, O1 =20, O2 = 10. Model 2 Maximizing Customer Reach Max Customer Reach = 139600, when T1 =10, T2 = 4, R1 = 15, R2 = 13, O1 =20, O2 = 35. 3
Slack & General Solution Model 1 Maximizing Exposure Rating Slack Analysis General Solution Max 90T1 + 55T2 + 25R1 + 20R2 + 10 O1 + 5 O2 Subject to: 2 R1+ 2 R2 - T1- T2 - S1 =0 Radio advertisement Lower bound 1000 O1 + 1000 O2 - S2 = 30000 Online budget Lower bound 4000 T1 + 1500 T2 +2000 R1 + 1200 R2 + 1000 O1 + 800 O1 - S3= 100000 Customer Reach 10000 T1 + 10000 T2 - S4 = 140000 TV budget Lower bound T1 + S5 =10 Television first 10 ads R1 + S6 =15 Radio first 15 ads O1+ S7 =20 Online first 20 ads 10000T1 + 10000T2 +3000R1 + 3000R2 + 1000 O1 + 1000 O2 + S8 =279000 Total Budget 3000 R1 + 3000 R2+ S9 = 99000 Radio Budget Upper bound T1 + T2 + S10 = 20 TV Advertisements Upper bound T1, T2, R1, R2, O1, O2 >= 0 Non-Negative 4
Sensitivity Report Model 1 Maximizing Exposure Rating The objective function coefficient for T1 is 90, with an allowable increase of \$ 1E+30 and an allowable decrease of 35. Therefore, as long as the profit contribution associated with T1 is between 90 + (1E+30) = 10^30 + 90 (a very big number) and 90 -35 = 55, the optimal solution for T1, T2, R1, R2, O1, O2 will not change. The shadow price for the Total Budget Constraint is 0.0055. In other words, if we increase the right-hand side of the Total Budget constraint by 1, the value of the optimal solution (Total exposure rate) will increase by 0.0055. Conversely, if we decrease the right-hand side of the Total Budget constraint by 1, the value of the optimal solution will decrease by 0.0055. 5
Managerial Report Question 1 A schedule showing the recommended number of television, radio, and online advertisements and the budget allocation for each medium. Show the total exposure and indicate the total number of potential new customers reached.