A manufacturer has used linear programming to determine the optimum production mix of the various TV models it produces. Recent information received by the manufacturer indicates that there is a 40% chance that the supplier of a component used in one of the models may raise the price by $35. The manufacturer thus can either continue to use the original (optimum) product mix (A1) or use a new ( optimum) mix based on the higher component price (A2). Naturally, action A1 is ideal if the price is not raised, and action A2 will also be ideal if the price is raised. The following table provides the resulting total profit per month as a function of the action taken and the random outcome regarding the component price.

(a) Develop the associated decision tree, and determine which action should be adopted.

(b) The manufacturer can invest $1000 to obtain additional information about whether or not the price will increase. This information says that there is a 58% chance that the probability of price increase will be .9 and a 42% chance that the probability of price increase will be .3. Would you recommend the additional investment?

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Original mix (A1) New mix (A2) Price increase (01) No price increase (02) $400,000 $372,000 $295,500 $350,000