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arnold2619
21.07.2020 •
Mathematics
An entertainment services provider on the internet has 10000 subscribers paying $15 per month. It can get 1000 more subscribers for each $1 decrease in the monthly fee. Determine the monthly fee that will yield the maximum monthly revenue and the value of that revenue
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Ответ:
Monthly fee that will yield the maximum monthly revenue is $12.5
Then the value of the maximum monthly revenue is $156 250
Step-by-step explanation:
x - value of decrease
1000x - number of new subscribers for $x decrease
10000+1000x - number of subscribers after $x decrease in the monthly fee
15-1x the monthly fee after $x decrease
f(x) = (10000 + 1000x)(15 - x) ← quadratic function
For quadratic function given in standard form: f(x) =a(x-h)²+k where a<0 the f(x)=k is the maximum value of function, and occurs for x=h
Expressing given function to standard form:
f(x) = 1000(10 + x)(15 - x)
f(x) = 1000(150 - 10x + 15x - x²)
f(x) = 1000(-x² + 5x + 150)
f(x) = -1000x² + 5000x + 150000 {a=-1000<0}
15-2.5 = 12.5
Ответ: