document.write( "Question 802033: Hello tutor,\r
\n" ); document.write( "\n" ); document.write( "Can you please help me solve this following problem.\r
\n" ); document.write( "\n" ); document.write( "The revenue function for a gourmet cupcake is given by R(x)=-40x^2+15x+350, where x is the price of one cupcake in a dollars. The cost function is C(x)=150-5x. Determine the price of one cupcake that will allow the bakery to break even. \r
\n" ); document.write( "\n" ); document.write( "Thanks. \n" ); document.write( "
Algebra.Com's Answer #483751 by ankor@dixie-net.com(22740)\"\" \"About 
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The revenue function for a gourmet cupcake is given by R(x)=-40x^2+15x+350, where x is the price of one cupcake in a dollars.
\n" ); document.write( " The cost function is C(x)=150-5x.
\n" ); document.write( "Determine the price of one cupcake that will allow the bakery to break even.
\n" ); document.write( ":
\n" ); document.write( "Breakeven occurs when cost = revenue, therefore
\n" ); document.write( "150 - 5x = -40x^2 + 15x + 350
\n" ); document.write( "Combine like terms on the left
\n" ); document.write( "40x^2 - 5x - 15x + 150 - 350 = 0
\n" ); document.write( "40x^2 - 20x - 200 = 0
\n" ); document.write( "Simplify, divide by 20
\n" ); document.write( "2x^2 - x - 10 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(2x-5)(x+2) = 0
\n" ); document.write( "the positive solution is all we want here
\n" ); document.write( "2x = 5
\n" ); document.write( "x = $2.50!
\n" ); document.write( ":
\n" ); document.write( "See if that works
\n" ); document.write( "150-5(2.5) = $137.50 in cost
\n" ); document.write( "and
\n" ); document.write( "-40(2.5^2) + 15(2.5) + 350 = 137.5
\n" ); document.write( "-250 + 37.5 + 350 = $137.50 in revenue \n" ); document.write( "
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