BUS 190 Professor Czerwinski Homework 14 1. Video Tech is considering marketing one of two new video games for the coming season: Battle Pacific or Space Pirates. Battle Pacific is a unique game and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand are as follows: Demand Battle Pacific High Medium Low Profit $1000 $700 $300 Probability 0.2 0.5 0.3 Video Tech is optimistic about its Space Pirates game. However, the concern is that profitability will be affected by a competitor's introduction of a video game viewed as similar to Space Pirates. Estimated profits (in thousands of dollars) with and without competition are as follows Demand Space Pirates With Competition Profit Probability High $800 0.3 Medium Low $400 $200 0.4 0.3 Space Pirates Without Competition High Medium Low Profit $1600 $800 $400 Probability 0.5 0.3 0.2 Video Tech believes there is a 0.6 probability that its competitor will produce a new game similar to space Pirates. a) Draw a decision tree and fold it back to find the optimal solution. b) What is the optimal decision? What is its expected value? c) Right now the chance of competition is 60%. How much higher or lower would this probability need to be in order for your decision to change? 2015 David Czerwinski 2. 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 Gallery's chief auctioneer's 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. 3. McDonald's 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 McDonald's 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? 2015 David Czerwinski