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GalinKa [24]
3 years ago
12

You operate a gaming website, www.mudbeast.net, where users must pay a small fee to log on. When you charged $4 the demand was 5

40 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? $
Mathematics
1 answer:
sertanlavr [38]3 years ago
5 0
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

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




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enrollment in the ski/snowboard club increased by 30% this year. there are now 182 students in the club. how many students were
eduard
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of means multipy so
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iragen [17]

Answer: The length of AC is 18 ft.

Step-by-step explanation:

By the given diagram,

AM = MB and CN = NB

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By the alternative interior angle theorem,

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