Question: 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 ........-2 ...........9 ..................7 .........-1
Option ...............-1 .........8 ..........-2 ..................9 ..........12
Toss sweep .........6 ........16 .........-5 ..................3 ..........14
Draw ..................-2 ........4 ...........3 ..................10 .........-3
Pass ....................8 ........20 .........12 .................-7 .........-8
Screen ................-5 .......-2 ..........8 ...................3 ...........16

a. If the coaches employ an offensive game plan, they will use the maximax criterion. What will their best play be?
b. If the coaches employ an offensive game plan, they will use the maximin criterion. What will their best play be?
c. What will their best offensive play be if State is equally likely to use any of its five defenses?
d. What will their best offensive play be if they use the Hurwicz criterion (with alpha = 0.4)?