The owner of a ski shop must order skis for the upcoming season. Orders must be placed in quantities of 25 pairs of skis. The cost per pair of skis is $50 if 25 are ordered, $45 if 50 are ordered, and...

The owner of a ski shop must order skis for the upcoming season. Orders must be placed in quantities of 25 pairs of skis. The cost per pair of skis is $50 if 25 are ordered, $45 if 50 are ordered, and $40 if 75 are ordered. The skis will be sold at $75 per pair. Any skis left over at the end of the year can be sold (for sure) at $25 a pair. If the owner runs out of skis during the season, he will suffer a loss of "goodwill" among unsatisfied customers. He rates this loss at $5 per unsatisfied customer. For simplicity, the owner feels that demand for the skis will be 30, 40, 50 or 60 pair of skis, with probabilities 0.2, 0.4, 0.2, and 0.2, respectively.

(a) Describe. sll, 0, the loss matrix, and the prior distribution.

(b) Which actions are admissible?

(c) What is the Bayes action?

(d) What is the minimax non randomized action?