U Toys has decided to launch the Professor Action Figure (PAF) as part of its Spring 2018 Action Figure Collection. A key component of the PAF is an electronic audio module that causes the action figure to spout some of his catch phrases when you squeeze his right hand. U Toys is considering whether to buy the audio modules from an outside supplier, or set up and manufacture the audio modules themselves. U Toys can purchase the audio modules for $10 each from an outside supplier. If instead they make the audio modules, there would be a one-time $40,000 setup cost, but the unit cost would then be just $5 each.
If demand for the PAF is high, U Toys projects they will need 12,000 audio modules. If demand for PAF is low, U Toys projects they will only need 5000 audio modules. U Toys believes there is a 40% chance that demand will be high and a 60% chance that demand will be low. However, they wouldn't find out the level of demand until well after PAF is in production and the decision on how to obtain the audio modules has been made.
Suppose that before making the make-or-buy decision, U Toys has the option to conduct a survey at a cost of $2000, to assess consumer attitudes about PAF. The results of this survey will indicate either a favorable or unfavorable attitude toward PAF. U Toys has conducted such a survey for other similar products thirty times in the past. Typically (but not always) a favorable attitude on the survey has meant demand will likely be high, while an unfavorable attitude has meant demand will likely be low. The results for the past thirty times the survey has been used are shown below.
Survey Results Favorable Unfavorable
High Demand 9 3
Low Demand 6 12
a. Label the first spreadsheet tab as ab, and on this worksheet use TreePlan to construct a single decision tree to help U Toys decide the course of action that would minimize the total expected cost associated with acquiring enough audio modules to meet the demand for the PAF (including setup and manufacturing costs if they make the audio modules, purchasing cost if they purchase the audio modules, and the cost of the survey if they conduct the survey). Then, in words below the tree, answer the following three questions: Should U Toys conduct the survey? Should they make or buy the audio modules? What is the total expected cost associated with the audio modules?
b. If the survey did not cost $2000, but rather cost $x, what is the largest value of $x for which it would be worthwhile to conduct the survey? Answer this question on spreadsheet tab ab, directly below your answer to part a.
c. Make a copy of spreadsheet tab ab used to solve parts a and b, by holding down control (or option on a Mac) while clicking and dragging tab ab to the right to make a copy of it. Double-click on the new tab and rename it to c. Now suppose U Toys is risk averse and wishes to take this into account when making this decision. U Toys would just barely be willing to accept a hypothetical 50-50 gamble that would net $50,000 if it succeeds but lose $25,000 thousand if it fails. Using TreePlan and the exponential utility function, re-solve the decision tree in spreadsheet tab c. Then, in words below the tree, answer the following two questions: Should U Toys conduct the survey? Should they make or buy the audio modules??TreePlan Range Name Bug: If you assign a cell a range name, and then change some of the Options in the TreePlan dialog box, TreePlan may delete the assigned range name. The workaround is to go back and redefine the range name after changing options (or wait to define range names until after choosing the appropriate options in TreePlan Options).