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

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

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!