Problem 3

The Los Gatos Art Gallery has a valuable painting that it wishes to sell at auction. There will be three bidders for the painting. The first bidder will bid on Monday, the second will bid on Tuesday, and the third will bid on Wednesday. Each bid must be accepted or rejected before the next bidder bids. If all three bids are rejected, the painting will be sold for a standing offer of $900,000. The Art Gallerys chief auctioneers estimates for the bid probabilities are contained in the table below:

Amount of Bid	Bidder 1 (Monday)	Bidder 2 (Tuesday)	Bidder 3 (Wednesday)
$1,000,000	0.0	0.0	0.7
$2,000,000	0.5	0.9	0.0
$3,000,000	0.5	0.0	0.0
$4,000,000	0.0	0.1	0.3

For example, the auctioneer has estimated that the likelihood that the second bidder will bid $2,000,000 is 90%.

(a) Use a decision tree to determine the optimal decision strategy for which bid to accept.

(b) Draw a risk profile for the optimal decision.

Problem 4

McDonalds is planning on opening a new location. They must decide how big of a restaurant to build at the location: small, medium, or large. Demand for the McDonalds in this location is uncertain, and will affect profitability. They have projected profitability for weak, moderate, and strong demand as shown in the following table:

Demand
Size	Weak	Moderate	Strong
Small	400	500	660
Medium	-250	650	800
Large	-400	580	990

(a) Compute the worst case profit for each restaurant size. What size restaurant should be built using a conservative decision criterion?

(b) Compute the best case profit for each restaurant size. What size restaurant should be built using an aggressive decision criterion?

(c) Compute the regret for each scenario and the maximum regret for each restaurant size. What size restaurant should be built to minimize the maximum regret?