You operate a gaming website. When you charged 3 dollars the demand was 570 log

Question

You operate a gaming website. When you charged 3 dollars the demand was 570 log ons per month. When you lowwere the price to 2.50 the demand increases to 855 log ons per month. Construct a linear demand function for your website and hence obtain the monthly revenue R as a function of the log on fee x You operate a gaming website. When you charged 3 dollars the demand was 570 log ons per month. When you lowwere the price to 2.50 the demand increases to 855 log ons per month. Construct a linear demand function for your website and hence obtain the monthly revenue R as a function of the log on fee x

Explanation / Answer

In order to find the linear demand function we would use the point slope form :

The point slope form is : (y - y1) = m(x - x1)

where m is the slope of the line , m = (y2 - y1)/(x2 - x1)

and (x1 , y1) is any point on the line

Let's get back to our problem

Let x represent the cost of 1 log on

and let y represent the demand

When we charged $3 the demand was 570 log on's

=> One point on the linear demand function is : (3 , 570)

When we lowered the price to $ 2.50 the demand was 855 log on's

=> Another point on the linear demand function is : (2.5 , 855)

Lets find the slope, m = (y2 - y1)/(x2 - x1) = (855 - 570)/(2.5 -3) = - 570

and (x1 , y1) = (3 , 570)

=> The linear demand function is:

(y - 570) = -570(x - 3)

or y = -570x + 2280   ---------> This is the required linear demand function

We know that Revenue is = Cost per unit * total number of units produced

                                      R(x) = x*y

                                      R(x) = x(-570x + 2280)

=> R(x) = -570x^2 + 2280x   ---------> This is the required revenue function

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