1) For the 2 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas.

24

1 2

For row player R:

r₁=

r₂=

For column player C:

c₁=

c₂=

Find the value v of the game for row player R.

V =

2) 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 increase by $900 if there is no infestation, but they decrease by $500 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 $600 per acre. Otherwise, her profits remain at their usual levels.

No worms{ }

Worms{ }

No 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? = $[ ] per acre.