Dave's revenue $R on the sale of widgets is determined by the formula

R = 35x - x^2

His cost $C for producing x widgets is given by the formula C = 5x + 30. For what values of x is Dave's profit positive?

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- Aug 2nd 2006, 08:18 PMpashahRevenue from sales
Dave's revenue $R on the sale of widgets is determined by the formula

R = 35x - x^2

His cost $C for producing x widgets is given by the formula C = 5x + 30. For what values of x is Dave's profit positive? - Aug 2nd 2006, 10:33 PMCaptainBlackQuote:

Originally Posted by**pashah**

$\displaystyle

(35x-x^2)-(5x+30)=-x^2+30x-30 >0

$

RonL - Aug 2nd 2006, 10:37 PMrgep
You need to determine the values of x for which C = 5x + 30 is less than R = 35x - x^2. The critical values of x for which C=R are the solutions to 35x - x^2 = 5x + 30, or x^2 - 30x + 30 = 0: these are 15 +- sqrt(195) or approximately 28.96 and 1.04. Since x has to be an integer the range of values for which C is less than R is 2 <= x <= 28.