document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114400>Question 1114400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A concession stand sells drinks at an event. When they sell the drinks for $1.50, they sell approximately 3,000. When they increased the price to $1.75, they only sold about 2,500 (assume linear). If it costs $0.40 to purchase each drink and $1,000 per event to rent the space...\r<BR>\n" );
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document.write( "1) How much should they sell the drinks for in order to maximize their profits? </SPAN>\n" );
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document.write( "When they sell the drinks for $1.50, their profit is $1.50-$0.40 = $1.10.  At that price, they sell 3000 drinks.<br><BR>\n" );
document.write( "When they raise the price by $0.25, the number of drinks they sell drops by 500 to 2500.  We are to assume that relationship is linear -- i.e., raising the price another 25 cents will result in an addition reduction of 500 in the number of drinks sold.<br><BR>\n" );
document.write( "So if x is the number of times the price is increased by 25 cents, then the profit is<BR>\n" );
document.write( "(profit per drink) times (number of drinks) minus (fixed (rental) cost):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.10%2B.25x%29%283000-500x%29-1000+=+3300%2B750x-550x-125x%5E2-1000+=+-125x%5E2%2B200x%2B2300 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This is a quadratic equation; the maximum value is when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-200%29%2F%282%28-125%29%29+=+%28-200%29%2F-250+=+0.8 ALIGN=MIDDLE  ALT=\"x+=+%28-200%29%2F%282%28-125%29%29+=+%28-200%29%2F-250+=+0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The maximum profit will be achieved if they raise the price by 25 cents 0.8 times -- i.e., if they raise the price by 20 cents, to $1.70.<br><BR>\n" );
document.write( "Answer: The price at which they should sell the drinks to maximize profit is $1.70. </SPAN>\n" );
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