An Arizona Farmer operates an 1100 acre irrigated farm in the Red River
Valley of Arizona. His principal activities are raising wheat, alfalfa,
and beef. The Red River Valley Water Authority has just given its water
allotments for next year (the farmer was allotted 1500 acre-feet), and
the famer is busy preparing his production plan for next year. He
figures that beef prices will hold at around $980 per ton and that wheat
will sell at $8 per bushel. Best guesses are that he will be able to
sell alfalfa at $120 per ton, but if he needs more alfalfa to feed his
beef than he can raise, he will have to pay $150 per ton to get the
alfalfa to his feedlot.
Some technological features of the famer’s operation are
wheat yield, 70 bushels per acre; alfalfa yield, 4 tons per acre. Other
features are given in the following table:
Activity
Labor, Machine Cost ($)
Water Requirements (Acre-Ft)
Land Requirements (Acres)
Alfalfa Requirements (Tons)
1 acre of wheat
$80.00
2
1
1 acre of alfalfa
$100.00
3
1
1 ton of beef
$200.00
0.1
0.1
5
Help the farmer to come up with a good production for the coming year.
-- Questions based on the LP output:
- How much water is being used?
- How much beef is being produced?
- Does the famer buy or sell alfalfa?
- How much profit will the famer receive from the optimal operation of his farm?
- Among all possible activities the famer might take, which is most attractive and which least attractive?
- How much should the famer pay to acquire another acre-ft of water? another acre of land? What will he use the additional resource for?
- What happens to the optimal planting policy if the price of wheat triples and the labor and machinery costs for wheat planting decreases by 50%?
- What happens to the profit if both purchasing and selling prices of alfalfa increase by $2?
- The labor and machinery costs listed may vary by up to 20% in both directions. Discuss the potential change in the current planting policy.
- Do you suggest the famer to plant soybean, which currently sells for $5/bushel and each acre of land will produce 100 bushel of soybean. Other features of soybean is given below:
Activity
Labor, Machine Cost ($)
Water Requirements (Acre-Ft)
Land Requirements (Acres)
Alfalfa Requirements (Tons)
1 acre of soybean
$30
1
1
Click here: An Arizona Farmer operates an 1100 acre irrigated farm in the Red River Valley of Arizona
