optimization

[mika0]

In the planning of a coffee shop, we estimate that if there is seating for between 40 and 80 people, the daily profit will be $50 per seat. However, if the seating capacity is more than 80 places, the daily profit per seat will be decreased by $1 for each additional seat over 80. What should the seating capacity be in order to maximize the coffee shop’s total profit, please help me to solve it i dont havy any idea

 

[Ishuda]

In the planning of a coffee shop, we estimate that if there is seating for between 40 and 80 people, the daily profit will be $50 per seat. However, if the seating capacity is more than 80 places, the daily profit per seat will be decreased by $1 for each additional seat over 80. What should the seating capacity be in order to maximize the coffee shop’s total profit, please help me to solve it i dont havy any idea

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

As a hint, start assigning variables: Let P be the profit and s the number of seats. The profit is then given by
P(s) = 50 s, 40 \(\displaystyle \le\) s \(\displaystyle \le\) 80
P(s) = ..., 80 \(\displaystyle \le\) s

Get the function P for s greater than 80 and then maximize P.