Revenue from sales

• Aug 2nd 2006, 08:18 PM
pashah
Revenue 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 PM
CaptainBlack
Quote:

Originally Posted by pashah
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:

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

RonL
• Aug 2nd 2006, 10:37 PM
rgep
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.