document.write( "Question 1158572: Joe Klothes has determined that the profit function for selling x thousand pairs of shorts is P(x)= -5x^2+19x-12\r
\n" ); document.write( "\n" ); document.write( "a) How many pairs of shorts must the company sell to break even?\r
\n" ); document.write( "\n" ); document.write( "b) How many pairs of shorts must the company sell to be profitable?\r
\n" ); document.write( "\n" ); document.write( "c)HOw many pairs of shorts must the company sell to maximize profits? \n" ); document.write( "

Algebra.Com's Answer #781513 by Shin123(626) $\"\"$ $\"About$

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Solved by pluggable solver: Completing the Square for Quadratics

To complete the square for the quadratic $\"-5%2Ax%5E2%2B19%2Ax-12=0\"$ , we must first find a square which when expanded, has -5x² and 19x in it.
\n" ); document.write( "Factoring -5 from the left side gives $\"-5%28x%5E2-3.8%2Ax%2B2.4%29=0\"$ . $\"%28x-1.9%29%5E2\"$ is the square we are looking for. So we get $\"-5%28%28x-1.9%29%5E2-1.21%29=0\"$ .\n" ); document.write( "Taking the -1.21 out of the -5, we get $\"highlight%28-5%28x-1.9%29%5E2%2B6.05%29\"$ . Subtracting 6.05 from both sides, we get $\"-5%28%28x-1.9%29%5E2%29=-6.05\"$ . Since the right side is negative, there are no real solutions.

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a) They must sell 3,000 or 800 pairs of shorts to break even.
b) To be profitable, the expression $\"-5%28x-1.9%29%5E2\"$ must be greater than -6.05. $\"-5%28x-1.9%29%5E2%3E-6.05\"$ . $\"5%28x-1.9%29%5E2%3C6.05\"$ . $\"%28x-1.9%29%5E2%3C1.21\"$ . $\"-1.1%3Cx-1.9%3C1.1\"$ . $\"0.8%3Cx%3C3\"$ . They must sell a number of pants between 800 and 3,000 to be profitable.
c) To maximize profit, the expression $\"-5%28x-1.9%29%5E2%2B6.05\"$ need to be at its maximum. The square of any real number is nonnegative. the expression is maximized when $\"-5%28x-1.9%29%5E2\"$ is 0. This occurs when x=1.9. They must make 1,900 pairs of pants to maximize profit. \n" ); document.write( "

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