Algebra

posted by .

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.

  • Algebra -

    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

First Name
School Subject
Your Answer

Similar Questions

  1. 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) …
  2. 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 log-ons per month. When you lowered the price to $3.50, the demand increased to 765 log-ons per month. (a) Construct …
  3. 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. …
  4. 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. …
  5. 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. …
  6. 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 …
  7. 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 …
  8. 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 …
  9. Business Math

    3.) The demand equation for a certain product is q=500-40p+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 …
  10. Business Math

    3.) The demand equation for a certain product is q=500-40p+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 …

More Similar Questions