document.write( "Question 119225This question is from textbook Algebra 2
\n" ); document.write( ": It costs (20 + x) dollars to produce (x) number of products. If the products sell for (300 - 2x) dollars each, how many products should be produced each month to maximize profit? \n" ); document.write( "

Algebra.Com's Answer #87390 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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It costs (20 + x) dollars to produce (x) number of products. If the products sell for (300 - 2x) dollars each, how many products should be produced each month to maximize profit?
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\n" ); document.write( "Organize what we know here:
\n" ); document.write( ":
\n" ); document.write( "Cost for x items = (20+x)
\n" ); document.write( ":
\n" ); document.write( "Revenue per item = (300-2x)
\n" ); document.write( "Revenue for x items = x(300-x)
\n" ); document.write( ":
\n" ); document.write( "We know that profit is: Revenue - cost:
\n" ); document.write( "Write that equation where y = profit on x items
\n" ); document.write( "y = x(300-2x) - (20+x)
\n" ); document.write( "y = 300x - 2x^2 - 20 - x
\n" ); document.write( "y = 280x - 2x^2 - x
\n" ); document.write( "write it as a quadratic equation:
\n" ); document.write( "y = -2x^2 + 279x
\n" ); document.write( ":
\n" ); document.write( "Maximum profit occurs at the axis of symmetry, we can find that using
\n" ); document.write( "x = $\"%28-b%29%2F%282a%29\"$ where, in our equation, a = -2 and b = 279
\n" ); document.write( "x = $\"%28-279%29%2F%282%2A-2%29\"$
\n" ); document.write( "x = $\"%28-279%29%2F%28-4%29\"$
\n" ); document.write( "x = +69.75 items
\n" ); document.write( "We can't make .75 items, so say max profit when 70 items are made
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\n" ); document.write( "Did this make sense to you? Let me know.
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