Jose and Maria run a small surfboard shop in Rincon They mus

Jose and Maria run a small surf-board shop in Rincon. They must order surf-boards for the coming season. Orders for the surf-boards must be placed in quantities of twenty (20). The cost per surf-board is $70 if they order 20, $67 if they order 40, $65 if they order 60, and $64 if they order 80. The surf-boards will be sold for $100 each. Any surf-boards left over at the end of the season can be sold (for certain) at $45 each. If Jose and Maria run out of surfboards during the season, then they will suffer a loss of \"goodwill\" among their customers. They estimate this goodwill loss to be $5 per customer who was unable to buy a surf-board. Jose and Maria estimate that the demand for surf-boards this season will be 10, 30, 50, or 70 surf-boards with probabilities of 0.2, 0.4, 0.3, and 0.1 respectively. Explain how many surf-boards they should buy, based on the Expected Value Criterion, Minimax Criterion and the Maximax criterion. Which is more reliable and why?

Solution

Expected Value = x1p(x1) + x2p(x2) + x3p(x3) + x4p(x4)

Expected value = 10(0.2) + 30(0.4) + 50(0.3) + 0.1(70)

Expected value = 2+12+15+ 7 = 36

So, They need to buy either 20 or 40.

If they bought 20, then there is goodwill loss of 36-20 = 16 customers.

Total Profit = 20*100 - 20*70 - 16*5 =2000 - 1400 -80 = $520.

If they bought 40 then there is loss of 40-36= 4 boards.

Total profit = 36*100 - 40* 67 - 45*4 =3600 - 2680-180 = $840.

They get more profit if they bought 40 boards.