T1 number of television ads with a rating of 90 and

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T1= number of television ads with a rating of 90 and 4000 new customers T2= number of television ads with a rating of 55 and 1500 new customers R1= number of radio ads with a rating of 25 and 2000 new customers R2= number of radio ads with a rating of 20 and 1200 new customers N1= number of newspaper ads with a rating of 10 and 1000 new customers N2= number of newspaper ads with a rating of 5 and 800 new customers Objective Function and Constraints Max 90T1 + 55T2 + 25R1 + 20R2 + 10N1 + 5N2 s.t. T1 < 10 R1 < 15 N1 < 20 10,000T1 + 10,000T2 + 3,000R1 + 3,000R2 + 1,000N1 + 1,000N2 < 279,000 4,000T1 + 1,500T2 + 2,000R1 + 1,200R2 + 1,000N1 + 800N2 > 100,000 -2T1 + -2T2 + R1 + R2 > 0 T1 + T2 < 20 10,000T1 + 10,000T2 > 140,000 3,000R1 + 3,000R2 < 99,000 1,000N1 + 1,000N2 > 30,000 T1, T2, R1, R2, N1, N2 > 0 Optimal Solution : Budget Allocation: T1 = 10, T2 = 5; 10 + 5 = 15 Television ads 15 * 10,000 = $150,000 R1 = 15, R2 = 18; 15 + 18 = 33 Radio ads 33 * 3,000 = $99,000
N1 = 20, N2 = 10; 20 + 10 = 30 Newspaper ads 30 * 1,000 = $30,000 If $10,000 is added to budget: 10,000 * 0.0055(shadow price) = 55 points Part 4 Exposure: 90(10) + 55(4) + 25(15) + 20(13) + 10(20) + 5(35) = 2130

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