Represent the situation as a game and find the optimal strategy for each player.

Question

Represent the situation as a game and find the optimal strategy for each player. State your final answer in the terms of the original question. A farmer grows apples on her 600-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown" produce and her profits per acre increases by $600 if there is no infestation, but they decrease by $200 if there is. If she does use pesticides and there is an infestation, her crop is saved and the resulting apple shortage (since other farms are decimated) raises her profits by $400 per acre. Otherwise, her profits remain at their usual levels. How should she divide her farm into "pesticide-free" zone and a "pesticide-use" zone? (Round your answers to two decimal places.) The farmer should set aside acres for pesticide-free apples and use pesticide on the other acres. What will be her expected increase in profits per acre with this strategy? This strategy will increase her expected profits by $ per acre.

Explanation / Answer

This strategy would give a profit of = -$200 x 0 + $600 x 600 = $36,000

Answer: worm no worm No pesticides ($200) $600 Pesticides $400 0 so with mini-max criteria r1 = $0 r2 = $1 c1 = $1 c2 = $1 with mini max and V = $200 With no pesticides farmer should not cultivate his 600 hectare land. with pesticices all the land shoud be cultivated.

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