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 log-ons per month. When you lowered the price to $2.50, the demand increased to 780 log-ons per month.
(a) Construct a linear demand function for your Web site and hence obtain the monthly revenue R as a function of the log-on fee 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 log-on fee x.
[What formula do I use to solve this? How should I approach it?]
Determine the log-on fee you should charge to obtain the largest possible monthly profit.
[Do I plug in some number?]
What is the largest possible revenue?
[How do I find this?]
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
-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