document.write( "Question 1193939: A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $1400 on seed.\r
\n" ); document.write( "\n" ); document.write( "If crop B brings in a profit of $270 per acre, and crop A brings in a profit of $120 per acre, how many acres of each crop should the farmer plant to maximize her profit?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #826009 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A farmer is going to divide her 60 acre farm between two crops.
\n" ); document.write( "Seed for crop A costs $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $1400 on seed.
\n" ); document.write( "If crop B brings in a profit of $270 per acre, and crop A brings in a profit of $120 per acre,
\n" ); document.write( "how many acres of each crop should the farmer plant to maximize her profit?
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Seed for crop B is twice as expensive as seed for crop A, but gives the profit which is more than twice as big\r\n" );
document.write( "\r\n" );
document.write( "as the profit of crop A (compare  270/120 = 2.25  with  40/20 = 2 !).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +---------------------------------------------------------------+\r\n" );
document.write( "    |   THEREFORE, it is clear, that the most aggressive strategy   |\r\n" );
document.write( "    |   is to sow as much area with crop B as possible.             |\r\n" );
document.write( "    +---------------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The possible area to sow with crop B, within the budget, is  1400/40 = 35 acres.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the most profitable solution is to sow 35 acres with crop B and do not sow crop A, at all.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The expected profit is then  35*270 = 9450 dollars, and it is maximal possible profit at given conditions.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );