Qdm Case Two

Assingment #2

Case Problem 1: Planning an Advertising Campaign

1. Summary of the Optimal Solution

T1 + T2 = 10 + 5 = 15 Television advertisements

R1 + R2 = 15 + 18 = 33 Radio advertisements

N1 + N2 = 20 + 10 = 30 Newspaper advertisements

Advertising Schedule: Media Number of Ads Budget

Television 15 $150,000

Radio 33 99,000

Newspaper 30 30,000

Totals 78 $279,000

Total Exposure Rating: 2,160

Total New Customers Reached: 127,100 (Surplus constraint 5)

2.

The dual price shows that total exposure increases 0.006 points for each one dollar increase in the advertising budget. Right Hand Side Ranges show this dual price applies for a budget increase of up to $294,000 - $279,000 = $15,000. So the dual price applies for the $10,000 increase. Total Exposure Rating would increase by 10,000(0.006) = 60 points A $10,000 increase in the advertising budget is a 3.6% increase. But, it only provides a 2.8% increase in total exposure. Management may choose that the additional exposure is not worth the cost. This is a discussion point.

3.

The ranges for the exposure rating of 90 for the first 10 television ads show that the answer remains optimal as long as the exposure rating is 55 or higher. This shows that the solution is not very sensitive to the exposure rating HJ has provided. Indeed, we would draw the same conclusion after reviewing the following four ranges. We could determine that Flamingo does not have to be concerned about the exact exposure rating. The only concern might be the newspaper exposure rating of 5. A rating of 5.5 or better can be expected to alter the current optimal solution.

4.

Remove constraint #5 for the linear programming model and use it to develop the objective function:

MAX 4000T1+1500T2+2000R1+1200R2+1000N1+800N2

Solving provides the following Optimal Solution

T1 + T2 = 10 + 4 = 14 Television advertisements

R1 + R2 = 15 + 13 = 28 Radio advertisements

N1 + N2 = 20 + 35 = 55 Newspaper advertisements

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