document.write( "Question 593978: A small farm has 70 acres of space to plant. The farmer wants to grow corn and green beans. It costs $60 per acre to grow the corn and $30 per acre to grow the green beans. The farmer has $1800 to use for planting the vegetables. It takes the farmer 3 days to plant each acre of corn and 4 days to plant each acre of green beans. There are 120 days available to plant the vegetables. When the farmer sells the vegetables, he can expect to make a profit of $180 per acre for the corn and $100 per acre for the green beans. How many acres should the farmer allow for each vegetable in order to maximize profit?\r
\n" ); document.write( "\n" ); document.write( "What are the equations I should use to solve this problem? \n" ); document.write( "
Algebra.Com's Answer #376589 by ankor@dixie-net.com(22740)\"\" \"About 
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A small farm has 70 acres of space to plant.
\n" ); document.write( " The farmer wants to grow corn and green beans.
\n" ); document.write( " It costs $60 per acre to grow the corn and $30 per acre to grow the green beans.
\n" ); document.write( " The farmer has $1800 to use for planting the vegetables.
\n" ); document.write( " It takes the farmer 3 days to plant each acre of corn and 4 days to plant each acre of green beans.
\n" ); document.write( " There are 120 days available to plant the vegetables.
\n" ); document.write( " When the farmer sells the vegetables, he can expect to make a profit of $180 per acre for the corn and $100 per acre for the green beans.
\n" ); document.write( " How many acres should the farmer allow for each vegetable in order to maximize profit?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of acres for corn
\n" ); document.write( "Let y = no. of acres for beans
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each constraint, put each equation the slope intercept for for graphing
\n" ); document.write( ":
\n" ); document.write( "The Acerage equation
\n" ); document.write( "x + y =< 70
\n" ); document.write( "y = -x + 70, (Red)
\n" ); document.write( ":
\n" ); document.write( "Cost equation
\n" ); document.write( "60x + 30y =< 1800
\n" ); document.write( "30y = -60x + 1800
\n" ); document.write( "y = -2x + 60, Green
\n" ); document.write( ":
\n" ); document.write( "Time equation
\n" ); document.write( "3x + 4y =< 120
\n" ); document.write( "4y = -3x + 120
\n" ); document.write( "y = -.75x + 30 (blue)
\n" ); document.write( ":
\n" ); document.write( "Obviously, all values are positive
\n" ); document.write( "x => 0
\n" ); document.write( "y => 0
\n" ); document.write( ";
\n" ); document.write( "Graph all 3 equations on the same grid
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-20%2C+90%2C+-20%2C+100%2C+-x%2B70%2C+-2x%2B60%2C+-.75x%2B30+%29+\"
\n" ); document.write( ":
\n" ); document.write( "From the graph we can see an intersection at x = 24, y = 12
\n" ); document.write( "Check and you can see these values will give us a cost of $1800 and time of 120 days
\n" ); document.write( "We can ignore the acreage equation, only 36 acres can be planted
\n" ); document.write( ":
\n" ); document.write( "\"When the farmer sells the vegetables, he can expect to make a profit of $180 per acre for the corn and $100 per acre for the green beans.\"
\n" ); document.write( "Profit:
\n" ); document.write( "24(180) + 12(100) =
\n" ); document.write( "4320 + 1200 = $5520 max profit
\n" ); document.write( ":
\n" ); document.write( "But another corner is x=30, y=0; 30 acres of corn and no beans
\n" ); document.write( "It also will cost $1800 and but only 90 days to plant
\n" ); document.write( "Profit: 30(180) = $5400, slightly less, but less time required
\n" ); document.write( ":
\n" ); document.write( "You can check the 3rd corner. x = 0; y = 30, 30 acres of beans and no corn \n" ); document.write( "
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