Jason D. answered • 04/11/19

University of California Graduate and Business Professional

let revenue = (price)(#tickets sold)

so f(x)=(20+x)(70-x),

where x represents the number of dollars increased in the price of a ticket, and -x happens to represent how one ticket sale is lost per one dollar increase in ticket price.

multiplying the above function out, the general form of this equation is as follows:

f(x) -x^{2} + 50x + 1400,

where a=-1, b=50, and c=1400

the max value of such a function is expressed like so:

MAX= c - (b^{2}/4a)

So, we have MAX= 1400 - (2500/(-4))

**or MAX=2025**

This addresses part B of the question.

Similarly, -b/2a gives us the x-value when f(x) is at its maximum value.

we've got x= -50/(-2), or **x=25**

**Therefore, at an optimal price of $25/ticket, we make a maximum revenue of $2,025**