document.write( "Question 1203118: The price $p$ and the quantity x sold of a small flat-screen television set obeys the demand equation below.
\n" ); document.write( "a) How much should be charged for the television set if there are 50 television sets in stock?
\n" ); document.write( "b) What quantity $x$ will maximize revenue? What is the maximum revenue?
\n" ); document.write( "c) What price should be charged in order to maximize revenue?
\n" ); document.write( "\[p=-.11 x+242\] \n" ); document.write( "

Algebra.Com's Answer #838424 by ikleyn(52932) $\"\"$ $\"About$

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\n" ); document.write( "The price p and the quantity x sold of a small flat-screen television set obeys the demand equation below.
\n" ); document.write( "a) How much should be charged for the television set if there are 50 television sets in stock?
\n" ); document.write( "b) What quantity $x$ will maximize revenue? What is the maximum revenue?
\n" ); document.write( "c) What price should be charged in order to maximize revenue?
\n" ); document.write( "p = -0.11x+242.
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document.write( "(a) To answer question (a), simply substitute the value of x= 50 into the given formula\r\n" );
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document.write( "         How much should be charged for the television set = -0.11*50 + 242 = 236.5.\r\n" );
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document.write( "(b) The revenue is this quadratic function\r\n" );
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document.write( "        Revenue = p*x = (-0.11x+242)*x.\r\n" );
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document.write( "    It has zeroes (x-intercepts) at x= 0 and x=  = 2200.\r\n" );
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document.write( "    The maximum of this quadratic function is at half-way between the x-intercepts,\r\n" );
document.write( "    which is  = 2200/2 = 1100.\r\n" );
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document.write( "    The maximum revenue is  1100*(-0.11*1100+242) = 133100.\r\n" );
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document.write( "(c)  To answer question (c), simply substitute the value of  x =  = 1100 into the given formula\r\n" );
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document.write( "         the price to charge in order to maximize revenue = -0.11*1100 + 242 = 121.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full.\r
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