A car dealership needs to determine how to allocate its $20000 advertising budget. They have estimated the expected profit from each dollar (X) spent in four different advertising media as follows:
Medium Expected Profit
Newspaper 100X^0.7
Radio 125X^0.65
TV 180X^0.6
Direct Mail 250X^0.5
If the company wants to spend at least $500 on each medium, how should it allocate its advertising budget to maximize profit?