You operate a gaming Web site, www. mudbeast. net, where users must pay a small fee to log on. When you charged $3 the demand was 1100 log-ons per month. When you lowered the price to $2.50, the demand increased to 1375 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 $30 to maintain your site. Express your monthly profit P as a function of the log-on fee x.
C) Determine the log-on fee you should charge to obtain the largest possible monthly profit. What is the largest possible monthly profit?

A) The linear relation between price and demand is:

The revenue R is:

B) The profit functionP is:

C) The largest monthly profit is obtained with a log-on fee of $2.5 per month. This corresponds to a profit of $3407.5.

Step-by-step explanation:

We have a site where the number of log-ons depends on our monthly fee. A linear relation is established between the price (log-on fee) and the number of log-ons.

We have two points for this linear relationship:

We will model the relation:

We can calculate the slope m as:

Then, replacing one point in the linear equation, we can calculate the intercept b:

Then, the linear relation between demand and price is:

The revenue R can be expressed as the multiplication of the price and the demand:

If we have a fixed cost of $30 per month, the profit P is:

We can maximize the profit by deriving the profit function and making it equal to zero.

This corresponds to a profit of:

below

step-by-step explanation:

1. 5/1

2. 10/16

3. 90/2

4. 1/20

5. 3/1

6. 14/24

7. 1/4

8. 18/10