Algebra
posted by Erin .
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.

Algebra 
Steve
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
Respond to this Question
Similar Questions

math
Logarithm!!! Select all of the following that are true statements: (a) log(2x) = log(2) + log(x) (b) log(3x) = 3 log(x) (c) log(12y) = 2 log(2) + log(3y) (d) log(5y) = log(20y) – log(4) (e) log(x) = log(5x) – log(5) (f) ln(25) … 
math
You operate a gaming Web site, where users must pay a small fee to log on. When you charged $4 the demand was 510 logons per month. When you lowered the price to $3.50, the demand increased to 765 logons per month. (a) Construct … 
economics
1. Chipo has the following utility function of 2 goods Pies (X) and fanta (Y): U= log X + log Y. (a) show that the consumer maximizes utility subject to the budget constraint. (b) derive the demand functions of good X and good Y. 2. … 
economics
1. Chipo has the following utility function of 2 goods Pies (X) and fanta (Y): U= log X + log Y. (a) show that the consumer maximizes utility subject to the budget constraint. (b) derive the demand functions of good X and good Y. 2. … 
economics
1. Chipo has the following utility function of 2 goods Pies (X) and fanta (Y): U= log X + log Y. (a) show that the consumer maximizes utility subject to the budget constraint. (b) derive the demand functions of good X and good Y. 2. … 
Economics
Very confused on how to figure these out. Suppose that the following table shows the weekly visits to an amusement park as a function of the daily admission fee charged: #visits daily fee 200 $50 400 $40 600 $30 800 $20 1000 $10 What … 
Calc
The demand for a commodity generally decreases as the price is raised. Suppose that the demand for oil (per capita per year) is D(p)=800/p barrels, where p is the price per barrel in dollars. Find the demand when p=55. Estimate the … 
Math
The demand for a commodity generally decreases as the price is raised. Suppose that the demand for oil (per capita per year) is D(p)=800/p barrels, where p is the price per barrel in dollars. Find the demand when p=55. Estimate the … 
Business Math
3.) The demand equation for a certain product is q=50040p+p^2 where p is the price per unit (in dollars) and q is the quantity of units demanded (in thousands). Find the point elasticity of demand when p = 15. If this price of 15 … 
Business Math
3.) The demand equation for a certain product is q=50040p+p^2 here p is the price per unit (in dollars) and q is the quantity of units demanded (in thousands). Find the point elasticity of demand when p = 15. If this price of 15 is …