Let s be the number of subscribers. Then the price is $25 minus 0.1 * (s-1000)/10. So the revenue for the tv company is given by:

I assume you can find the maximum of this function by setting the derivative to zero. The answer is s=1750.

But that assumes the price is changing continuously with the number of subscribers, which is only an approximation. To get the exact answer, we should calculate some values around 1750. We can reduce the amount of work by recognizing that the answer must end in 9.

s=1739, R=30780.3

s=1749, R=30782.4

s=1759, R=30782.5

s=1769, R=30780.6

So the answer is s=1759.

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- Hollywood