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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.)

 Apr 29, 2019
 #1
avatar+106539 
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Let  x be the salary earned in thousands and the take-home pay  = T  ......so we have....

 

T  =  x -  (x/100)(x)  =   -x^2 / 100  +  x

 

The salary that maximizes the take-home pay  is   -1 / [ 2 * (-1/100) ] =  100/2  = 50 ⇒ $50,000

 

[ The take-home pay = $25,000 ]

 

 

cool cool cool

 Apr 29, 2019

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