Q 2: If the ticket agency charges ‘p’ dollars per ticket for a concert, it can sell maximum of (40000 – p) tickets. Find:
a. A polynomial to represent the total revenue with a ticket price as p dollars.
b. How many tickets will be sold for a price of $10 each.
c. Total revenue if the price of each ticket is $10.
a. p(4000-p)
b. 40000-10=39,990
c. 10(39990)=399,900
To solve this problem, let's break it down step by step:
a. To represent the total revenue with a ticket price of p dollars, we need to multiply the ticket price by the number of tickets sold. The number of tickets sold can be calculated as (40000 - p). Therefore, the polynomial to represent the total revenue is:
Revenue(p) = p * (40000 - p)
b. To find the number of tickets sold for a price of $10 each, we substitute p = 10 into the polynomial we found in part a:
Revenue(10) = 10 * (40000 - 10)
Simplifying this equation will give us the total revenue when the ticket price is $10.
c. To find the total revenue if the price of each ticket is $10, we substitute p = 10 into the polynomial we found in part a:
Revenue(10) = 10 * (40000 - 10)
Again, simplifying this equation will give us the total revenue when the ticket price is $10.