Baseline information Billboard advertising cost: $100 per week Sales margin: $5

Question

Baseline information

Billboard advertising cost: $100 per week

Sales margin: $5

Profit = sales margin * sales # - billboard ad expense

Sales # = sum (x=0 to 40) [ purchase probability * individuals of x exposures]

Purchase probability =0.7* [1 – exp ( -0.15 * exposure #)]+0.1

Calculate purchase probability up to 40 exposures

a

Compute the number of sales when the billboard campaign duration is 3 weeks (t=3).

b

Find the optimal duration of t that can maximizes its profit.

x f_x 0 48 1 37 2 30 3 24 4 20 5 16 6 13 7 11 8 9 9 7 10 6 11 5 12 5 13 3 14 3 15 2 16 2 17 2 18 1 19 1 20 2 21 1 22 1 23 1

Explanation / Answer

Using:

Billboard advertising cost: $100 per week

Sales margin: $5

Profit = sales margin * sales # - billboard ad expense

Sales # = sum (x=0 to 40) [ purchase probability * individuals of x exposures]

Purchase probability =0.7* [1 – exp ( -0.15 * exposure #)]+0.1

Calculate purchase probability up to 40 exposures

A.

The no of sales is

No of sales is 625.45

Duration 3 Billboard ad Cost 100 Sales Margin 5 Exposure # Purchase prob Sales # Profit 0 0.100 0.00 2827.26 5*Sales #-(100*3) 1 0.198 0.20 2 0.281 0.56 3 0.354 1.06 4 0.416 1.66 5 0.469 2.35 6 0.515 3.09 7 0.555 3.89 8 0.589 4.71 9 0.619 5.57 10 0.644 6.44 11 0.666 7.32 12 0.684 8.21 13 0.700 9.11 14 0.714 10.00 15 0.726 10.89 16 0.736 11.78 17 0.745 12.67 18 0.753 13.55 19 0.760 14.43 20 0.765 15.30 21 0.770 16.17 22 0.774 17.03 23 0.778 17.89 24 0.781 18.74 25 0.784 19.59 26 0.786 20.43 27 0.788 21.27 28 0.790 22.11 29 0.791 22.94 30 0.792 23.77 31 0.793 24.59 32 0.794 25.42 33 0.795 26.24 34 0.796 27.05 35 0.796 27.87 36 0.797 28.69 37 0.797 29.50 38 0.798 30.31 39 0.798 31.12 40 0.798 31.93 625.45

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