Answer:
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
