Chapter 10, Problem 31RE

Agriculture A farmer decides each spring whether to plant com or soybeans. Com is the better crop under wet conditions, soybeans under dry conditions. The following payoff matrix has been determined, where the entries are in tens of thousands of dollars.

$\begin{array}{l}\text{ Weather(fate)}\\ \begin{array}{cc}\text{Wet}& \text{Dry}\end{array}\\ \text{Farmer}\begin{array}{c}\text{Corn}\\ \text{Soyabeans}\end{array}\left[\begin{array}{cc}8& 4\\ 2& 10\end{array}\right]\end{array}$

Use linear programming and the simplex method to find optimal strategies for the farmer and the weather.