The net monthly profit, in dollars, from the sale of a certain item is given by the formula P(x) = 10^6[1 + (x-1)e^0.001x], where x is the number of items sold. Determine the number of items that yield the maximum profit. At full capacity, the factory can produce 2000 items per month.

Expert Answers

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When in doubt take the derivative using the product property.


P'(x)=0 when (0.001x+0.999)=0

Solving for x =-999.  This is the only critical points, but it is not possible to make -999 items.

We also have to check x=0 and x=2000



` `The solution is to produce 2000 items.

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