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 a linear demand function for your website and hence obtain the monthly revenue R as a function of the log-on fee x.

Vorbeckenuc 2022-07-27 Answered
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 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 $10 to maintain your site. Express your monthly profit P as a function of the log-on fee x.
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?
$ ?
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Answers (1)

Marisa Colon
Answered 2022-07-28 Author has 18 answers
Step 1
- when you charged $4, demand was 540 log-ons per month,
- when you charged $3.50, demand was 810 log-ons per month.
a) Consider linear demand function, D q = m q + b, where q is quantity.
Here we have two ordered pairs (540,4) and (810,3.5) first, we calculate slope of demand function.
m = 3.5 4 810 540 = 0.5 270 = 0.00185
D q = 0.00185 q + b
for (540,4), we have, 4 = ( 0.00185 ) 540 + b
4 = 0.99 + b b = 4.99
D 1 = 0.00185 q + 4.99 i . e . , R ( x ) = 0.00185 x + 4.99 is monthly
revenue R as function of log-on fee x.
Step 2
b) If internet provides charges a monthly fee of $10, so, here R ( x ) = $ 10, we have to find x.
10 = 0.00185 x + 4.99 x = $ 2708
monthly profit P as function of log-on fee x.
is P ( x ) = 4.99 R ( x ) 0.00185 = 2697.29 540.54 R ( x )
P ( x ) = 2697.29 540.54 R ( x )
If R ( x ) = 0, largest possible monthly profit P(x) will be maximum.
largest   P ( x ) = $ 2697.29

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