a. Identify this problem as a set of equations defining the objective function and constraints. 

b. Graph at least 2 objective function lines and identify the optimal solution. 

c. From the graph, approximate the optimal combination of the decision variables and the optimal value. 

d. Algebraically solve the model above. Identify the optimal combination of the decision variables and the optimal value. 

e. Compare the algebraic solution with the graphical solution. What are the differences? Why do they occur?

The Punxsutawney Phil Farm raises and supplies wild game to several private hunting clubs nearby. The farm produces two species: slow pigs, and quick groundhogs. The farm has 800 acres of land and an operating budget of $7500 per year. A pig takes 3 acres of land to raise to a huntable size, and groundhogs need 3.3 acres of land for foraging and nesting. Annual supplemental feed and health care run $17 per pig and $11 per ground hog. The farm manager’s son, Ben Williams, tends and feeds the animals. He especially likes ground hogs, since his day is never ending. Anyway, it takes Sam an average of 3.0 hours per pig and 5.0 hours per groundhog. Ben can work up to 1700 hours per year, but at the very least his father requires him to work at least 900 hours per year. The farm has a long-term contract to sell at least 300 pigs per year. Further, Ben has a fondness for breeding clones of Punxsutawney Phil so want to sell at least 35 groundhogs per year. The manager can sell the pigs for $31 each, and groundhogs for $44 each and want to maximize annual sales from the farm.