| Excel Companion Chapter 5 section 7 |
| Response Functions in Marketing | Response.xls |
Open the file Response.xls.
SITUATION:
A company is about to launch a new product that will sell for
$5.00. Research prepared by the marketing division includes data
on probable customer response to a promotion campaign that will
last for t days. The estimated upper level of potential customers
is 80,000.
The response function r(t) gives the proportion of these
potential customers that will respond to the promotion within t
days and has been estimated to be r(t) = 0.50( 1 - e -0.02t). Verify that about 20% of the
potential customers will respond by buying the product after 25
days and after 50 days this will increase to 32%.
The expected revenue after t days is the response function r(t) times the size of the market times the unit price. The revenue function, R(t), is the product 80,000 * 5* r(t) = 400,000* r(t). The variable cost of running the promotion is $400 per day and the fixed cost is $15,000. Total cost is C(t) = 400*t + 15,000. Profit after t days is R(t) - C(t). The marketing division's objective is to run the promotional campaign for the number of days that will maximize profit.
If we set the lower value of t to 2 and also set the t
increment to 2 then we observe that the revenue, cost, and profit
functions all increase during the first 100 days.
Copyright © Joseph F. Aieta, Babson
College 1997
