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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.
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 400-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 increase by $500 if there is no infestation, but they decrease by $100 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 $200 per acre. Otherwise, her profits remain at their usual levels.
No worms Worms
Pesticides ________ ________
Pesticides ________ ________
r1 = _____
r2 = _____
c1 = _____
c2 = _____
v =
How should she divide her farm into a "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.
