document.write( "Question 1026350: The demand equation for a microwave is p = 140 – 0.001x where p is the unit price in dollars and x is the number of units produced and sold. The cost equation for the microwave is C = 40x + 150,000 where C is the total cost in dollars and x is the number of units produced. The total profit P obtained by producing and selling x units is given by P = R – C = xp – C. Is there a price p that yields a profit of $3 million? Explain your answer. \n" ); document.write( "
Algebra.Com's Answer #641603 by ankor@dixie-net.com(22740)\"\" \"About 
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The demand equation for a microwave is p = 140 – 0.001x where p is the unit price in dollars and x is the number of units produced and sold.
\n" ); document.write( " The cost equation for the microwave is C = 40x + 150,000 where C is the total cost in dollars and x is the number of units produced.
\n" ); document.write( " The total profit P obtained by producing and selling x units is given by P = R – C = xp – C. Is there a price p that yields a profit of $3 million?
\n" ); document.write( ":
\n" ); document.write( "Revenue (px) - cost = 3 million
\n" ); document.write( "x(140-.001x) - (40x + 150000) = 3,000,000
\n" ); document.write( "140x - .001x^2 - 40x - 150000 = 3000000
\n" ); document.write( "-.001x^2 + 140x - 40x = 3000000 + 150000
\n" ); document.write( "-.001x^2 + 100x - 3150000 = 0
\n" ); document.write( "This is a quadratic equation, find x that gives us the maximum
\n" ); document.write( "x = -b/(2a) where b=100 and a = -.001
\n" ); document.write( "x = \"%28-100%29%2F%282%2A-.001%29\"
\n" ); document.write( "x = 50000 units for max profit
\n" ); document.write( "Find the actual profit when 50000 are made
\n" ); document.write( "-.001(50000^2) + 100(50000) = $2,500,000 is max profit; the answer is no. \n" ); document.write( "
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