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In a certain city the rate of taxation is the following: x% tax is collected for an income of x thousand dollars. What income, in dollars, will yield the greatest take home pay? (Take-home pay is the income minus the tax on that income.)

 Dec 6, 2018
 #1
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x - x/100 *x

-1/100 x^2 + x 

 

Take derivative = 0

-2/100 x +1 = 0

2/100 x = -1

x = 100/2 = 50           So 50 thousand will net take home $25 000.

 Dec 6, 2018

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