SOLUTION: The total profit function P(x) for a company producing x thousand units is given by P(x) = -3x2 + 60x - 225. Find the values of x for which the company makes a profit

Algebra ->  Inequalities -> SOLUTION: The total profit function P(x) for a company producing x thousand units is given by P(x) = -3x2 + 60x - 225. Find the values of x for which the company makes a profit      Log On


   

Question 380630: The total profit function P(x) for a company producing x thousand units is given by
P(x) = -3x2 + 60x - 225.
Find the values of x for which the company makes a profit
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
P(x) = -3x2 + 60x - 225.
P(x) = -3[x^2-20x+75]
P(x) = -3[x-15][x-5]

Find the values of x for which the company makes a profit
Solve -3(x-15)(x-5) > 0
Boundary values are x = 5 and x = 15
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Find solution values for the inequality by checking values:
Check x = 0,the P(x)=-225 : not an inequality solution
Check x = 10 to get -3*-5*5> 0 solutions in 5< x < 10
Check x = 20 to get -3*+5*+15<0 so no solutions in (15,+inf)
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Ans: Profit for (5,15)
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graph%28400%2C300%2C-10%2C50%2C-100%2C100%2C-3x%5E2%2B60x-225%29
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Cheers,
Stan H.