SOLUTION: Brian's revenue R in dollars from the sale of x baseball souvenirs is determined by the formula R=20x-x^2. His cost C in dollars is given by the formula C=-19x+140. For what values

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Brian's revenue R in dollars from the sale of x baseball souvenirs is determined by the formula R=20x-x^2. His cost C in dollars is given by the formula C=-19x+140. For what values      Log On


   

Question 884682: Brian's revenue R in dollars from the sale of x baseball souvenirs is determined by the formula R=20x-x^2. His cost C in dollars is given by the formula C=-19x+140. For what values of x is Brian's profit positive? Write your answer in complete sentences.
Answer by lwsshak3(11628) About Me  (Show Source):
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Brian's revenue R in dollars from the sale of x baseball souvenirs is determined by the formula R=20x-x^2. His cost C in dollars is given by the formula C=-19x+140. For what values of x is Brian's profit positive? Write your answer in complete sentences.
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profit=revenue-cost=(20x-x^2)-(-19x+140)
P(x)=20x-x^2+19x-140>0
P(x)=-x^2+39x-140>0
P(x)=-(x^2-39x+140>0
P(x)=-(x-4)(x-35)>0
number line:
<...-...4.....+....35....-.....>
what values of x is Brian's profit positive? (4,35), that is, all values of x between 4 and 35