A company runs food service concessions for sporting events throughout the country. Their marketing research department chose a particular football stadium to test market a new jumbo hot dog. It was found that the demand for the new hot dog is given approximately by

Question

p=6−ln(x),5≤x≤500,
where x is the number of hot dogs (in thousands) that can be sold during one game at a price of p dollars. If the company pays 1 dollar for each hot dog, how should the hot dogs be priced to maximize the profit per game?

Write a formula for the profit as a function of the number x of hot dogs sold.
Profit =(Value of x)
Number of hot dogs that maximizes profit:

Answer 1

profit=x(p-1)
profit=x(6-lnx)
profit=6x-xlnx
dprofit/dx=0=6-lnx-x/x
lnx=6-2=5
x=e^5
x=148 *thousand)