1. A recording company has produced a new compact disk featuring a very popular recording group. Before launching a national sales campaign, the marketing research department chose to test market the CD in a Kisumu city. Their interest is in determining the length of a sales campaign that will maximize total profits. From the empirical data, the research department estimates that the proportion of a target group of 50,000 persons buying the CD after t days of television promotions is given by:

(1-e^-0.03t)

If Sh.4(in Sh.00) is received for each CD sold, then the total revenue after t days of promotion will be approximated by:

R(t)=(4)(50000)(1-e^-0.03t=2000(1-e^-0.03t) t>0

Television promotion costs are:C(t)=4000+3000t t>0

How many days of television promotion should be used to maximize total profit?