A manufacturing company found that the equation f(x)=-3.2x^2+268.2x+257 could be used to approximate their profit per day for x items produced.

How many objects would need to be made to get a profit of $5423?
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1 Answer

5423=-3.2x²+268.2x+257, 3.2x²-268.2x+5166=0.

x²-83.8125x+1614.375=0

x=(83.8125±√83.8125²-6457.5)/2=(83.8125±23.8125)/2=53.8125 or 30.

The minimum quantity is 30.

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