Question 204208
The profit function for a computer company is given by P(x) = -x^2+ 25x - 24 where x is the number of units produced (in thousands) and the profit is in thousand of dollars.
a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit.
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Maximum profit occurs when x = -b/2a = -25/(2*-1) = 12.5
 
(thousands of) units =12.5  
maximum profit = -12.5^2+25*12.5 - 24 = 132.5 thousand dollars
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b) Determine how many units should be produced for a profit of at least 40 thousand.
-x^2+25x - 24 >= 40
-x^2+25x-64 = 0
 x = [-25 +- sqrt(625 - 4*-1*-64)]/(-2)
x = [-25 +- sqrt(369)]/-2
x = [-25 +- 19.209]/-2
x = 22.1 or x = 2.89
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more than 2.89(thousands of) units 
less than 22.1(thousands of) units 
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Cheers,
Stan H.