Question

vụI YES, Question 2. [10 points) The owner of a baseball team and local stadium has commissioned a study that showed the demand by fans for stadium seats (per playing date) to be P = 22 -0.2Q, where P is the average price of a ticket and Q represents the number of seats (expressed in thousands). The local stadium seats a maximum of 56,000 per game. Suppose the owner offers you 10% of the revenues. If you can only choose a uniform per-ticket price, what is the maximum amount you can earn per game? (Note: Assume that all seats and all games are the same in this problem.)

Answer 1

Demand by fans for stadium seats,  

P = 22 -0.2Q

It is given that the owner offers me 10% of the revenue earned. So if I maximize owner’s total revenue then it will also maximize my revenue.

Let $1585288955751_blob.png$ = Total revenue of the Owner.

Or,

= PQ

Or,

n = (22Q -0.20)

Or,

n = 220 - 0.202

Now maximizing $1585288955824_blob.png$ with respect to Q

Or,

06 = 22 – 0.4Q = 0

Or,

忍

Since the local stadium has a maximum capacity of 56000 per game so accommodating 55000 persons won’t be any problem. So Q = 55 is feasible.

So, when Q = 55, P = 22 – 0.2Q = 22 – 0.2*55 = 11

Therefore total revenue earned by the owner,

T = 11 * 55000 = 605000

So the maximum amount I can earn =

| 10 605000 = 60500 元多而= 0