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A company has started selling a new type of smartphone at the price of $120 - 0.1x where x is the number of smartphones manufactured per day. The parts for each smartphone cost $60 and the labor and overhead for running the plant cost $4000 per day. How many smartphones should the company manufacture and sell per day to maximize profit?

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MissPhiladelphia
We derive an equation for the the profit:
P = (120 - 0.1x)x - (60x + 4000)
P = -0.1x² + 60x - 4000

To maximize profit, we differentiate in terms of x and equate to zero:
-0.2x + 60 = 0
x = 300

The company should produce 300 smartphones per day.

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