Algebra
posted by Erin on .
You operate a gaming Web site, where users must pay a small fee to log on. When you charged $3 the demand was 520 logons per month. When you lowered the price to $2.50, the demand increased to 780 logons per month.
(a) Construct a linear demand function for your Web site and hence obtain the monthly revenue R as a function of the logon fee x.
R(x)=
(b) Your Internet provider charges you a monthly fee of $10 to maintain your site. Express your monthly profit P as a function of the logon fee x.
P(x)=
[What formula do I use to solve this? How should I approach it?]
Determine the logon fee you should charge to obtain the largest possible monthly profit.
x=$
[Do I plug in some number?]
What is the largest possible revenue?
[How do I find this?]
Thank you.

If we have a linear demand function, it will look like
R = mx+b where x is the price and y is the demand at that price.
780 = 2.5m + b
520 = 3m + b
so,
260 = .5m
m = 520
b = 2080
R = 2080  520x
profit = revenue  cost
revenue = demand * price
P = R*x  10
P = 2080x  520x^2  10
you have a parabola, where the vertex is at x =
b/2a = 2080/1040 = 2
P(2) = 2070