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3 years ago

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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

1 answer:

zepelin [54]3 years ago

5 0

Answer:

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

$h=\frac{-b}{2a}\ ,\quad k=f(h)$

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}

$h=\dfrac{-5000}{2\cdot(-1000)}=\dfrac{5000}{2000}=\dfrac52=2.5\\\\k=f(2.5)=1000(10+2.5)(15-2.5)=1000\cdot12.5\cdot12.5=156\,250$

15-2.5 = 12.5

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melomori [17]

Let numbers of books be 'b' and numbers of CDs be 'c'

We can set up two equations:
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We are solving for the number of books and the number of CDs bought

When we have two equations in terms of two different variables; $b$ and $c$ , that we need to solve, then this becomes a simultaneous equation problem.

First, rearrange Equation [1] to make either $b$ or $c$ the subject:
$b+c=20$
$b=20-c$

Then we substitute $b=20-c$ into Equation [2]
$1.50b+5c=54.50$
$1.50(20-c)+5c=54.50$
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Now we know the value of $c$ which is $c=7$ , substitute this value into $b=20-c$ we have $b=20-7=13$

Answer:
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3 years ago