document.write( "Question 192640: Suppose that a corporation that manufactures widgets determines that its revenue function is R(x)=1000x-x^2 and its cost function is C(x)=3000+20x, where x represents the number of widgets produced. Find the corporation's maximum profit. \n" ); document.write( "
Algebra.Com's Answer #144681 by ankor@dixie-net.com(22740)\"\" \"About 
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Suppose that a corporation that manufactures widgets determines that
\n" ); document.write( " its revenue function is R(x)=1000x-x^2 and its cost function is C(x)=3000+20x,
\n" ); document.write( " where x represents the number of widgets produced.
\n" ); document.write( "Find the corporation's maximum profit.
\n" ); document.write( ":
\n" ); document.write( "Profit = Revenue - cost
\n" ); document.write( "therefore:
\n" ); document.write( "P = (1000x - x^2) - (3000+20x)
\n" ); document.write( "P = 1000x - x^2 - 3000 - 20x
\n" ); document.write( "P = -x^2 + 980x - 3000;
\n" ); document.write( "A quadratic equation, find the axis of symmetry & maximum using x = \"%28-b%29%2F%282a%29\"
\n" ); document.write( "In this equation: a=-1; b=980
\n" ); document.write( "x = \"%28-980%29%2F%282%2A-1%29\"
\n" ); document.write( "x = +490 units produce max profit
\n" ); document.write( ":
\n" ); document.write( "Find max profit using: P = -x^2 + 980x - 3000;
\n" ); document.write( ":
\n" ); document.write( "P = -(490^2) + 980(490) - 3000
\n" ); document.write( "P = -240100 + 480200 - 3000
\n" ); document.write( "P = $237,100 is max profit
\n" ); document.write( ":
\n" ); document.write( "You can check the math by substituting 490 for x in the original equations \n" ); document.write( "
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