Scenario 1: The Occupational Safety and Health Administration (OSHA) has recently announced it will award an $85,000 research grant to the company submitting the best proposal for using wireless communications technology to enhance safety in the coal mining industry. Thomas Edmunds, the owner of TeleGadget, a small communications research firm located just outside of Warrensburg, New York, is considering whether or not to apply for this grant. Tom estimates he would spend approximately $5,000 preparing his proposal and that he has about a 5050 chance of receiving the grant. If he is awarded the grant, he would need to decide whether to use microwave, cellular, or infrared technology. He has some experience in all three areas, but would need to acquire some new equipment depending on which technology is used. The cost of the equipment needed for each technology is as follows: Besides equipment costs, Tom knows he will spend money in research and development (R\&D) to carry out the research proposal, but he does not know exactly what the R&D costs will be. For simplicity, he estimates the following best-case and worst-case R&D costs for each technology, and assigns probabilities to each outcome based on his degree of expertise: Tom needs to consider all the factors in the problem to decide whether or not to submit a grant proposal to OSHA. (a) Create a decision tree for this problem. Which course of action maximizes the EMV? (b) Create the corresponding risk profile. Would you still follow the approach from part (a) after seeing the risk profile? Explain. (c) How small would the probability of receiving the grant have to be for it to no longer be wise to submit the grant proposal? (Hint: use Excel Solver.) (d) Create a strategy table for this problem (using a two-way Data Table) by varying both the probability of receiving the grant (from 0 to 1 in 0.1 increments) and the probability of high infrared R&D costs (from 0 to 0.5 in 0.1 increments). What are the main takeaways from this table? 1. What number does your second (from left to right) decision node show inside it? 2. What is the EMV from part (a) in the problem statement? 3. From the risk profile created for part (b) of the problem, what is the probability Thomas will lose money if he follows the tree's recommendation? 4. What is the answer to part (c) of the problem statement? Type this answer in with four, rather than two, digits after the decimal point (rounded as usual). 5. Consider the strategy table built for part (d) in the problem. Let 0 represent "Do not apply for the grant," 1 represent "Apply and go with microwave," 2 represent "Apply and go with cellular," and 3 represent "Apply and go with infrared." When the probability of receiving the grant is 0.3 and the probability of high infrared costs is 0.2 , what does your strategy table recommend you do? (Answer with 0,1,2, or 3.)
