Payoff table and maximin

A manager has to decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot if poor quality (s1), 50% chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).

s1        s2            s3

a1                   20        30            90

a2                   60        70            10

a3                   80        50            40

What is the numerical value of the maximin?

Maximin is the largest of a set of minima.  For each choice a1 a2 or a3 there is a minimum payoff respectively 20 10 and 40.  The choice a3 is the largest of those minima.  It ensures that the minimum payoff is 40 and it could be as high as 80.  The maximin is 40.

It doesn't seem realistic for the payoff to be 40 when rejecting a lot of good quality.  And you would think that the manager should decide based on some kind of testing, even a sample of 1.

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