A software company will sell N(x) copies of a new app it has developed if it spends $x on advertising. You are given N(x)=80x -0.2x^2 + 800 . Find the maximum number of copies that can be sold.
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To find the maximum number of copies that can be sold, we need to determine the value of x for which N(x) reaches its maximum value.
We have the equation N(x) = 80x - 0.2x^2 + 800.
To find the maximum value, we can take the derivative of N(x) with respect to x and set it equal to zero.
N'(x) = 80 - 0.4x = 0
Solving for x, we find:
0.4x = 80
x = 80 / 0.4
x = 200
Therefore, in order to maximize the number of copies sold, the software company should spend $200 on advertising.
Substituting x = 200 into the equation N(x), we find:
N(200) = 80(200) - 0.2(200^2) + 800
= 16000 - 0.2(40000) + 800
= 16000 - 8000 + 800
= 8800
Therefore, the maximum number of copies that can be sold is 8800.
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