Problem:

A row crop farmer is deciding how to allocate his acres between two crops, corn and soybeans. Currently, the farmer has $300$ hours of labor and $480$ pounds of nitrogen available. The farmer estimates that the labor requirement is $3$ hours for both an acre of corn and an acre of soybeans. Nitrogen requirements are $6$ pounds for an acre of corn and $3$ pounds for an acre of soybeans.

What would be the most profitable allocation of acres if the profit per acre of corn is $$3$ and the profit per acre of soybeans is $$2?$

Formulate an LP model that optimizes the allocation of resources and maximizes profits for the farmer. Also, create a graph and sketch the feasible region and label all axes, corner points, and feasible region.$(10$ points$)$

Variables:

Objective:

Constraints: