A university is trying to determine what price to charge for tickets to football games. At a price of $27 per ticket, attendance averages 40 comma 000 people per game. Every decrease of $3 adds 10 comma 000 people to the average number. Every person at the game spends an average of $6.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?

ticket price is 27 -3(3)= $18 , and Number of people = 40,000+10,000(3)=70,000 .

Step-by-step explanation:

We start the equation with (27-3x).  We don't know how many times we're subtracting $3 from the price.  This is multiplied by (40,000+10,000x). 

⇒

This represents the amount of money for tickets multiplied by the amount of people.  We still need to add the amount of concessions.  Since (40,000+10,000x) represents the number of people, we multiply that by $6.00.This gives us:

⇒

⇒

⇒

Differentiating this w.r.t x :

⇒

⇒

⇒ ,

⇒ , { Rounding off }

So, ticket price is 27 -3(3)= $18 , and Number of people = 40,000+10,000(3)=70,000 .

ok

step-by-step explanation:

practice. practice. practice.