The Tech football coaching staff has six basic plays it runsevery game.

The Tech football coaching staff has six basic plays it runsevery game. Tech has an upcoming game against State onSaturday, and the coaches know State employs five different defenses. The coaches have estimated the number ofyards 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 2 2 6 8 2
Option 3 7 1 10 16
Toss Sweep 5 14 5 6 12
Draw 2 3 2 8 7
Pass 10 20 12 7 6
Screen 5 3 8 7 16
If the coaches employ an offensive game plan, theywill use the maximax criterion. What will their bestplay be?
b. If the coaches employ a defensive plan, they will usethe maximin criterion. What will their best play be?
c. What will their best play be if State is equally likely touse any of its defenses?
d. The Tech coaches have reviewed game films and havedetermined the following probabilities that State will
use each of its defenses
Defense 54 63 Wide Tackle Nickel Blitz
Probability 0.40 -0.10- 0.20- 0.20- 0.10.Using expected value, rank Tech’s plays from best to worst. During the actual game, Tech has a third down and
10 yards to go and the coaches are 60% certain State willblitz, with a 10% chance of any of the other four defenses.
What play should Tech run, and is it likely Tech will make
the first down?

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