A TV cable company has subscribers who are each paying '%!! $ per month. It can get more subscribers for each $ decrease in the monthly fee. What #% "'! !Þ&! rate will yield maximum revenue, and what will this revenue be?

It will be replacing de gibberish codes with numbers to facilitate the calculation. Imagine that each are paying $14 per month and it can get 140 more subscribers for each $0.50 decrease in the monthly fee and they have 2800 subscribers.

Step-by-step explanation:

x = subscribers and y = the monthly fee

y=14

x=2800

P(revenue) =

14 × 2800 = 39 200

y = 14 - 0.5 × n

x = 2800 + 140 ×n

Therefore,

P(revenue) = x × y= (2800+140 × n) × (14 - 0.5 ×n)

= -70 × n² + 560 × n + 39 200

In order to find the max value, it is necessary to derivate the function to know the peak of variation. (dP/dn)=0

f'(P) = - 140 × n + 560

0 = - 140×n + 560  → n=4

so the optimal value is

y = 14 - (0.5 × 4) = 12 USD

x= 2 800 + (140×4 )= 3 360

Max profits

P= - 70 × 4² + (560 × 4) +39 200 = 40 320 USD

factor

Step-by-step explanation: