Question

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.
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 log-on fee x.
P(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.
x=$
[Do I plug in some number?]

What is the largest possible revenue?
[How do I find this?]

Thank you.

Answer 1

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