The proportion of people responding to a TV advertisement of a new product after it has been on the market for t days is given by :
P = 1 - e^-0.2t
The marketing area contains 10,000,000 potential customers and each response to the advertisement yields a gross profit of 70 cents (gross profit = sales - cost of good sold). The advertisement costs $30,000 to produce and $5000 for each day it runs.
A) Find the value of P when t is very large and interpret its meaning.
B)Find an expression for advertising costs over time and hence obtain an expression for net profits over time. (net profit = gross profit - advertising expenses)
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