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A restaurant sells about 330 sandwiches each day at a price of $6 each. For each $.25 decrease in price, 15 more sandwiches are sold per day. How much should the restaurant charge to maximize daily revenue? What is the maximum daily revenue?
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\n" ); document.write( "Let x = amt ($) decrease in price
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\n" ); document.write( "Since there is an increase of 15 for each $.25 decrease, $1 decrease: 4*15 = 60
\n" ); document.write( "Let 60x = increase in sandwiches sold
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\n" ); document.write( "Price = (6 - x)
\n" ); document.write( "Number sold = (330 + 60x)
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\n" ); document.write( "Revenue = price * number sold: Let y = Revenue:
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\n" ); document.write( "y = (6-x)(330+60x)
\n" ); document.write( "FOIL
\n" ); document.write( "y = 1980 + 360x -330x - 60x^2
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\n" ); document.write( "A quadratic equation:
\n" ); document.write( "y = -60x^2 + 30x + 1980
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\n" ); document.write( "Find the axis of symmetry: x = -b/(2a); a=-60; b=+30
\n" ); document.write( "x = -30/(2*-60)
\n" ); document.write( "x = -30/-120
\n" ); document.write( "x = +.25
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\n" ); document.write( "Max revenue occurs at 6 - .25 = $5.75 for the sandwich
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\n" ); document.write( "Find Max revenue: The problem states that for every $.25, they sell 15 more:
\n" ); document.write( "(330+15) * 5.75 = $1983.75 is the max revenue.
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\n" ); document.write( "You can also find max revenue by substituting .25 for x in the equation:
\n" ); document.write( "-60(.25^2) + 30(.25) + 1980 = 1983.75
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\n" ); document.write( "A graph would look like this:
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