You operate a gaming website, where users must pay a small fee to log on. when you charged $4 the demand was 540 log-ons per month. when you lowered the price to $3.50, the demand increased to 810 log-ons per month. (a) construct a linear demand function for your website 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 $30 to maintain your site. express your monthly profit p as a function of the log-on fee x. hint [see example 4.] p(x) = determine the log-on fee you should charge to obtain the largest possible monthly profit. x = $ what is the largest possible monthly profit? $

A) Demand function

price (x)          demand (D(x))

4                      540

3.50                  810

D - 540          810 - 540
= 
x - 4               3.50 - 4

D - 540
= - 540
x - 4

D - 540 = - 540(x - 4)

D = -540x + 2160 + 540

D = 2700 - 540x

D(x) = 2700 - 540x

Revenue function, R(x)

R(x) = price * demand = x * D(x)

R(x) = x* (2700 - 540x) = 2700x - 540x^2

b) Profit, P(x)

profit = revenue - cost

P(x) = R(x) - 30

P(x) = [2700x - 540x^2] - 30

P(x) = 2700x - 540x^2 - 30

Largest possible profit => vertex of the parabola

vertex of 2700x - 540x^2 - 30

When you calculate the vertex you find x = 5 /2

=> P(x) = 3345

you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)

Ithink it’s b, hope this .