Consider big jake’s problem: big jake operates a 1200-acre ranch in arizona. his principle activities are raising beef, wheat and alfalfa. the arizona water authority has just given its water allotments for next year (big jake was allotted 2000 acre-feet) and big jake is busy preparing his production plan for next year. he figures that beef prices will hold at around $600 per ton and he will make a profit of $60 per ton. wheat will sell at $1.60 per bushel and his profit will be $.60 per bushel. best guesses are that he will be able to sell alfalfa at $34 per ton and make a profit of $10 per ton

some technological features of big jake’s operation are wheat yield, 50 bushels per acre; alfalfa yield, 3 tons per acre. other features are given below. the variables are defined as follows:

activity costs water reqmts land reqmts

(acre-feet) (acres)

1 ac wheat $8 1.5 1.0

1 ac alfalfa 30 2.5 1.0

1 ton beef 40 0.1 0.05

a. what would be big jakes optimal planning strategy to obtain the maximum profit?

b. what happens to the optimal planting policy if the profit of wheat doubles?