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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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?
Profit is $\displaystyle R-C$ so the question is asking for what values of $\displaystyle x$ is:Quote:
Originally Posted by pashah
$\displaystyle
(35x-x^2)-(5x+30)=-x^2+30x-30 >0
$
RonL
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.
