This decision tree illustrates the expected profits and standard deviations associated with three decisions facing a mobile phone producer. All figures are in millions of dollars. The root node represents the decision of whether to produce the phones in China or North America. The second pair of nodes represents the decision of whether to market the phones in China or North America. The final nodes represent the choice of selling price: if the phones are sold in China, they will be sold for either $30 or $40, whereas if they are sold in North America, they will be sold for either $40 or $50. Based on these calculated values, what is the company's best strategy? - **Make in China:** - **Sell in China:** - $30: Mean = 1,250, SD = 750 - $40: Mean = 375, SD = 625 - **Sell in North America:** - $40: Mean = -1,000, SD = 1,500 - $50: Mean = -1,500, SD = 1,250 - **Make in North America:** - **Sell in China:** - $30: Mean = -1,500, SD = 1,250 - $40: Mean = -250, SD = 1,639 - **Sell in North America:** - $40: Mean = 1,250, SD = 2,137 - $50: Mean = -250, SD = 1,639 This decision tree helps to visualize the potential outcomes and associated risks for each possible production and sales strategy.

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As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are  P = 400,000 −400Q and  P = 900,000 −250Q, respectively. Your cost function is C(Q) = 125,000 + 430,000Q.   How many new homes should you build, and what profits can you expect? Number of homes you should build:  homes   Profits you can expect: $

Mega Studios is thinking of producing a megafilm which could be a megahit or a megaflop. Profit is uncertain for two reasons: (1) the cost of producing the film may be low or high, and (2) the market reception for the film may be strong or weak. There is a 0.6 chance of low costs (and a 0.4 chance of high costs). The probability of strong demand is 0.5 (the probability of weak demand is 0.5). The studio’s profits (in millions of dollars) for the four possible outcomes are shown in the table:     demand     strong weak cost low 80 10 high 0 -70   a) Should the studio produce the film? Justify your answer using expected profits. b) The studio is concerned that the film’s director might let production costs get out of control. Thus, the studio insists on a clause in the production contract giving it the right to terminate the project after the first $30 million is spent. By this time, the studio will know for certain whether total production costs are going to be low (i.e. under control)…