document.write( "Question 551695: If a farmer digs his potatoes today, he will have 100 bags worth $2 a bag. Every week he waits the crop increases by 10 bags and the price drops by 10 cents a bag. When should the farmer dig his potatoes in order to maximize his profit? \r
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Algebra.Com's Answer #359856 by ankor@dixie-net.com(22740)\"\" \"About 
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If a farmer digs his potatoes today, he will have 100 bags worth $2 a bag.
\n" ); document.write( " Every week he waits the crop increases by 10 bags and the price drops by 10 cents a bag.
\n" ); document.write( " When should the farmer dig his potatoes in order to maximize his profit?
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\n" ); document.write( "Let w = no. of weeks for max spuds (today, w=0)
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\n" ); document.write( "Profit = no. of bags * price per bag
\n" ); document.write( "P = (100 + 10w)(2.00 - .10w)
\n" ); document.write( "FOIL
\n" ); document.write( "P = 200 - 10w + 20w - w^2
\n" ); document.write( "a quadratic equation
\n" ); document.write( "f(w) = -w^2 + 10w + 200
\n" ); document.write( "max profit occurs at the axis of symmetry, x = -b/(2a); b=10, a=-1
\n" ); document.write( "w = \"%28-10%29%2F%282%2A-1%29\"
\n" ); document.write( "w = +5 weeks will yield max profit (which would be: 150 * 1.50 = $225)
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