My Notes Ask Your Teacher 7. 44 points WaneFMAC7 2.1.037 You operate a gaming we

Question

My Notes Ask Your Teacher 7. 44 points WaneFMAC7 2.1.037 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 580 log-ons per month. When you lowered the price to $3.50, the demand increased to 870 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 $20 to maintain your site. Express your monthly profit P as a function of the log-on fee x. HINT [See Example 4. P(x) Determine the log-on fee you should charge to obtain the largest possible monthly profit. x=$ What is the largest possible monthly profit?

Explanation / Answer

demand function is a linear function

( 4, 580 ) and ( 3.50 , 870 )

slope = (870 - 580 ) / 3.50 - 4

slope = -580

hence, the demand equaqtion is

R = x ( -580x + 2900 )

R = -580x^2 + 2900 x

b) profit = revenue - cost

so, we can write

P(x) = -580x^2 + 2900 x - 20

c) x max = -b/ 2a

= -2900 / 2 (-580 )

= 2.5

x = $ 2.5

d) largest possible monthly profit is

-580(2.5)^2 + 2900 (2.5) - 20

= $ 3605

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