R&D Project. Sullicooie Inc., is considering a $$5$ million research and development $($R&D$)$ project. Profit projections appear promising, but Sullicooie$$s president is con$-$cerned because the probability that the R&D project will be successful is only $0\mathrm{.}50.$ Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $$20$ million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $$25$ million. Under this option, the company would not build the $$20$ million production facility.The decision tree is shown in Figure $13\mathrm{.}18.$ The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $$59$ million. However, the cost of the R&D project $($$$5$ million$)$ and the cost of the production facility $($$$20$ million$)$ show the profit of this outcome to be $$592$$$52$ $$205$$$34$ million. Branch probabilities are also shown for the chance events. LO $1,3$a$.$Analyze the decision tree to determine whether the company should undertake the R&D project. If it does, and if the R&D project is successful, what should the com$-$pany do$?$ What is the expected value of your strategy?b$.$What must the selling price be for the company to consider selling the rights to the product?c$.$Develop a risk profile for the optimal strategy.