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# Farmer Jim's Decision Problem: Growing Wheat or Barley

Farmer Jim needs to decide how much wheat and barley to plant on his 100 ha (100 hectares, or ) of land. Wheat yields \$2/ha and takes 3 days of work/ha. Barley yields \$1/ha and takes 1 day of work/ha. He is a profit-maximizing farmer who has a maximum of 120 working days available.
The top slider explores how Jim's profits vary with the area of wheat planted, while the second slider explores how Jim's profits vary with the area of barley.
Why does the area of barley planted go down if the area for wheat is greater than 10 ha?
Why can he only grow a maximum of 40 ha of wheat?
How much wheat and barley will he plant?

### DETAILS

The linear programming (LP) formulation of this problem was discussed in the tutorial class, where is the area for wheat and is the area for barley. The problem setup is:
Maximize
subject to:
,
,
.
This model demonstrates the LP problem from Management Decision Tools (UWA unit SCIE3367/8367) tutorial 2_2011.

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