48 Alexis Cornby makes her living buying and selling corn.

On January 1, she has 50 tons of corn and $1,000. On the first day of each month Alexis can buy corn at the following prices per ton: January, $300; February, $350; March, $400;

April, $500. On the last day of each month, Alexis can sell corn at the following prices per ton: January, $250; February,

$400; March, $350; April, $550. Alexis stores her corn in a warehouse that can hold at most 100 tons of corn. She must be able to pay cash for all corn at the time of purchase. Use linear programming to determine how Alexis can maximize her cash on hand at the end of April.