I need help figuring out this math question. Please Help its due on Saturday!

Question

A University is trying to determine the price to charge for football games. At a price of $16 per ticket, 40000 people attend the game, while at $12 per ticket, 50000 people attend the game. On average, everyone spends $4.00 for concessions. The capacity of the stadium is 60000 people. With the information given, we wish to construct the price function , where x is the number of people in attendance at the stadium. From this, we wish to construct the revenue function , the total amount of money taken in at the stadium. We then wish to find the number of people that we wish to attend that will maximize the revenue, the maximum revenue, and finally the price to be charged per ticket to guarantee the maximum revenue. The capacity of the stadium is to be determined from the price function.

Answer 1

Graphically, two points are (Q,P) = (40,16) and d(50,12) with Q measured in thousand units

That's a slope of -4/10 = -2/5

y=mx+ b or

P=mQ+ b

P= (-2/5)Q + b, plug in either point to calculate b

12 = (-2/5)(50) + b

b = 32

equation is:

P= (-2/5)Q + 32

Revenue = R = PQ = [(-2/5)Q + 32]Q = -2Q^2/5 + 32Q

R' = -4Q/5 + 32 = 0

4Q/5 = 32

Q = (5/4)32 = 40 = revenue maximizing output

max R = PQ = [(-2/5)Q + 32] Q = (-16 +32)/40 = 16/40 = 2/5 x 1000 = $400