Problem $13-17($Algorithmic$)$

Hemmingway, Inc., is considering a $$7$ million research and development $($R&D$)$ project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only $0\mathrm{.}40.$ Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $$17$ 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 $$26$ million. Under this option, the company would not build the $$17$ million production facility.