<PRE><B>Question 161544</B>
A manufacturer finds that for the first 300 units of its product that are produced and sold, the profit is $60 per unit. The profit on each of the units beyond 300 is decreased by $0.10 times the number of additional units sold. What level of output will maximize profit?
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For the 1st 300, Profit = 300*60
For all over 300, the profit is $60 - $0.10 times the number sold, = $60 - $0.10*(x-300).
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Overall then, 
Profit = 300*60 + (x-300)*(60 - 0.1(x-300))
P = 18000 + (x-300)*(60 - 0.1x + 30)
P = 18000 + (x-300)*(-0.1x + 90)
P = 18000 -0.1x^2 + 120x - 27000
P = -0.1x^2 + 120x - 9000
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To find the max, set the 1st derivative = 0
0 = -0.2x + 120
0.2x = 120
x = 600 
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