document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120631>Question 1120631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fast food restaurant sells 200 Megaburger combos daily at $4.59 each. Every 10 cents procee increase reduces sales by 3 combo meals. Find the maximum income from Megaburger combo sales and the price for which they should be sold.  </SPAN>\n" );
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document.write( "Let's work the problem in cents instead of dollars to avoid having to work with the decimals....<br><BR>\n" );
document.write( "The current price is 459; at that price they sell 200 a day.  The total revenue is 200(459) = 91800, or $918.<br><BR>\n" );
document.write( "For each price increase of 10 cents, the number sold per day will decrease by 3.  So if the price increases by 10 cents x times, the price will be (459+10x) and the number sold will be (200-3x).<br><BR>\n" );
document.write( "The total revenue will then be<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28459%2B10x%29%28200-3x%29+=+-30x%5E2%2B623x%2B91800 ALIGN=MIDDLE  ALT=\"%28459%2B10x%29%28200-3x%29+=+-30x%5E2%2B623x%2B91800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The maximum value of a quadratic function ax^2+bx+c is when x = -b/2a.  For this problem, x = -623/-60 = 10.38.  Since x has to be a whole number, the maximum revenue will be when x=10.<br><BR>\n" );
document.write( "So the maximum revenue will be when the price is 459+10(10) = 559, or $5.59.  The revenue will be -30(10^2)+623(10)+91800 = 95030, or $950.30. </SPAN>\n" );
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