A cable TV company has 4000 customers paying $110 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.

can be solved by utilizing the derivative. We have 55-x = price 4000+100x = number of customers price * number of customers = profit (55-x)(4000+100x) = profit Expanding, we get = 55*4000 + 55*100x - 4000x - 100x^2

We now want the maximum possible value of this. To do so, we use the derivative and set it equal to zero. d/dx (-100x^2 + 1500x + 220000) = -200x + 1500 = 0 200x = 1500 x = 7.5

Thus the price that yields max revenue is 55 - 7.5 = 47.50 dollars And the max revenue is (47.5)(4750) = 225,625

andromache andromache · Answer 2 · 2022-01-20T08:37:51+01:00

The maximum revenue is 225,625

The calculation is as follows:

55-x = price

4000+100x = number of customers

price × number of customers = profit

(55-x)(4000+100x) = profit

Now

= 55 ×4000 + 55 × 100x - 4000x - 100x^2

Here we applied derivates

d/dx (-100x^2 + 1500x + 220000) = -200x + 1500 = 0

200x = 1500

x = 7.5

Thus the price that yields max revenue is 55 - 7.5 = 47.50 dollars

Now

And the max revenue is (47.5)(4750) = 225,625

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