document.write( "Question 181921: A local seafood shop sells lobster tails for $18 per tail. They sell an average 160 tails per week. Their research has determined that for each $0.50 decrease per tail, they would sell an additional 8 lobster tails per week. What should they charge per lobster tail to maximize their revenue? \n" ); document.write( "

Algebra.Com's Answer #136561 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A local seafood shop sells lobster tails for $18 per tail. They sell an average 160 tails per week. Their research has determined that for each $0.50 decrease per tail, they would sell an additional 8 lobster tails per week. What should they charge per lobster tail to maximize their revenue?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of 8 ea tails above 160 sold
\n" ); document.write( "Also x = no. of $.50 decreases from a cost of $18 per tail
\n" ); document.write( ":
\n" ); document.write( "Rev = no. sold * price
\n" ); document.write( "R = (160+8x)*(18-.5x)
\n" ); document.write( "FOIL
\n" ); document.write( "R = 2880 - 80x + 144x - 4x^2
\n" ); document.write( "R = -4x^2 + 64x + 2880
\n" ); document.write( ":
\n" ); document.write( "Find the axis of symmetry: x - $\"%28-b%29%2F%282a%29\"$
\n" ); document.write( "In this equation a=-4; b=64
\n" ); document.write( "x = $\"%28-64%29%2F%282%2A-4%29\"$
\n" ); document.write( "x = 8 ea $.50 decreases to for max sales
\n" ); document.write( ":
\n" ); document.write( "18 - (8*.50) $14 per tail for max revenue
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