For the following exercise, solve using the graphical method. Choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all corner points, and determine the solution that optimizes the objective function:
A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?
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