document.write( "Question 202987: A fruit grower has 150 acres of land available to raise two crops, A and B. It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days available each year for trimming. It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B, and there are 30 days per year available for picking. The profit is $140 per acre for crop A and $235 per acre for crop B. Determine the optimal acreage for each fruit and the optimal profit. (Show all your work including any graphs you used.) \n" ); document.write( "
Algebra.Com's Answer #153228 by ankor@dixie-net.com(22740)\"\" \"About 
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: A fruit grower has 150 acres of land available to raise two crops, A and B.
\n" ); document.write( " It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B,
\n" ); document.write( " and there are 240 days available each year for trimming.
\n" ); document.write( "It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B,
\n" ); document.write( "and there are 30 days per year available for picking.
\n" ); document.write( "The profit is $140 per acre for crop A and $235 per acre for crop B.
\n" ); document.write( "Determine the optimal acreage for each fruit and the optimal profit.
\n" ); document.write( "(Show all your work including any graphs you used.)
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement, rearrange for graphing:
\n" ); document.write( ":
\n" ); document.write( "\" A fruit grower has 150 acres of land available to raise two crops, A and B.\"
\n" ); document.write( "A + B = 150
\n" ); document.write( "A = 150-B; (red)
\n" ); document.write( ":
\n" ); document.write( "It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B,
\n" ); document.write( " and there are 240 days available each year for trimming.\"
\n" ); document.write( "1A + 2B = 240
\n" ); document.write( "A =< 240-2B; (green)
\n" ); document.write( ":
\n" ); document.write( "It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B,
\n" ); document.write( "and there are 30 days per year available for picking.\"
\n" ); document.write( ".3A + .1B = 30
\n" ); document.write( ".3A = 30 - .1B
\n" ); document.write( "A =< 100 -\"1%2F3\"B; (blue)
\n" ); document.write( ":
\n" ); document.write( "Graph these 3 equations, A on the y axis, B on the x axis
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-30%2C+150%2C+-13%2C+150%2C+150-x%2C+240-2x%2C+100-.33x%29+\"
\n" ); document.write( ":
\n" ); document.write( "The corner points of the area of feasibility:
\n" ); document.write( "1. A=100,B=0
\n" ); document.write( "2. A=75, B=75
\n" ); document.write( "3. A=60,B=90
\n" ); document.write( "4. A=0, B=120
\n" ); document.write( ":
\n" ); document.write( "The profit is $140 per acre for crop A and $235 per acre for crop B.
\n" ); document.write( "Find the values of these points:
\n" ); document.write( "1. 140(100) + 235(0) = $14,000
\n" ); document.write( "2. 140(75) + 235(75) = $28,125
\n" ); document.write( "3. 140(60) + 235(90) = $29,550
\n" ); document.write( "4. 140(0) + 235(120) = $28,200
\n" ); document.write( ":
\n" ); document.write( "Plant 60 acres of Plant A, and 90 acres of Plant B, for max profit
\n" ); document.write( " \n" ); document.write( "
\n" );