Problema Solution
The total revenue(= income money) that event ticket sales for this event would generate can be computed using the following.
R(x)= Total Revenue= (price per individual ticket)x(estimated number of tickets sold) = X * N(x)
N(x)= -10+850
Find a formula for the total revenue function r(X)in terms of the variable x. X=20
a) How much total revenue will be produced, if the tickets are priced at $25 each?
b) at what price should the tickets be priced in order to generate $17,500 total revenue?
c) Find the ticket price that will generate the maximum possible total revenue. and also state this max total revenue possible is for this event.
Maximum total revenue = ------------- occurs when the ticket price =
GRAPH the function R(x), Include the vertex and intercepts on the graph ( And show scales used
Answer provided by our tutors
(a) N(25) = -10*25 +850 = 600
R(25) = 25*N(25) = 25*600 = 15000
So the revenue is $15,000 if the tickets are priced at $25 each.
(b)
R(x) = x*N(x) =x(-10x+850) = 17,500
So
x(-10x+850) = 17,500
x = 35
So at the price of $35 the revenue will be $17,500
(c)
R(x) = x*N(x) =x(-10x+850) = -10(x^2 - 85x) = -10(x-47.5)^2 + 22562.5
So when x = 47.5, R = 22562.5
Maximum total revenue = $22,562.5, occurs when the ticket price =$47.5
(d)
Vertex: (47.5, 22562.5), intercept: (0,0) and (85, 0)