Systems, Matrices, and Determinants · Hard problem

A farmer has $100$ acres to plant with crops $A$ and $B$. Each acre of $A$ needs $\$40$ of seed and $2$ hours of labor; each acre of $B$ needs $\$60$ of seed and $1$ hour of labor. The farmer has $\$4800$ for seed and $140$ hours of labor. Profit is $\$100$ per acre of $A$ and $\$120$ per acre of $B$. Find the maximum possible profit, in dollars.