The Tech football coaching staff has six basic offensive plays it runs every game. Tech has an upcoming game against State on Saturday, and the Tech coaches know that State employs five different defenses. The coaches have estimated the number of yards Tech will gain with each play against each defense, as shown in the following payoff table:
Defense
Play 54 63 Wide Tackle Nickel Blitz
Off tackle 3 -29 7-1
Option -18 -2912 Toss sweep 6 16 -5314 Draw -24 3 10 -3
Pass 8 20 12 -7 -8
Screen -5 -28 316
a. If the coaches employ an offensive game plan, they will use the maximax criterion. What will be their best play?
b. If the coaches employ a defensive plan, they will use the maximin criterion. What will be their best play?
c. What will be their best offensive play if State is equally likely to use any of its five defenses?