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 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 With Competition Demand High Medium Low Profit $800 $400 $200 Probability 0.3 0.4 0.3 Without Competition Demand 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?