Farmer Joe would like to plant mallees (a type of eucalyptus) on his 90 ha of land (1 hectare = 1/100 ). However, he does not want to plant mallees on the fertile soils that are highly productive for wheat cropping (an area constraint). He knows that wheat profits are about $120/ha, while mallee will yield a profit of $90/ha. He also knows that mallees will cost him 2 days of work/ha, while wheat costs 3 days/ha. He is a profit-maximizing farmer who has a maximum of 180 working days available (labor constraint).
Use the sliders to explore how relaxing the two area constraints and the labor constraint affects the feasible area for a solution to Joe's problem.
Use the "profit" slider to explore how much profit Joe could possibly make, while staying within the feasible solution region.
Can you see at which basic solution corner his profit-maximizing solution exist? What is the limiting constraint?
This model demonstrates the LP problem from Management Decision Tools (UWA unit SCIE3367/8367) computer labs 2 and 3_2011.
The linear programming (LP) formulation of this problem was discussed in class for the example, where a maximum of 40 ha could be planted with mallees (less productive lands). The problem setup is:
This problem is based on real-life decision problems that farmers in Western Australia have to make. Oil mallees farming is emerging as a potential addition to dry-land agriculture systems. Planting mallees can generate income from carbon credits, from biofuels, and may also come with additional environmental benefits that improve farming practice.
Of course, the on-farm economics is very important for landholders when they decide whether to plant mallees or not, because there are costs associated with the initial plantings and they essentially take cropping land out of production.