A manufacturer of high$-$tech computing equipment must decide whether or not to continue development of a new promising technology. Continuing the development would cost $$2$ Million. If the development is continued, then a patent is either awarded or not. The best estimate is that there is a $70\%$ chance that the patent will be awarded and a $30\%$ chance that it will not.$$If the patent is awarded, the company needs to decide whether or not to license the technology. If it does, it would receive a total of $$25$ million in licensing royalties. However, the company could also produce and sell the technology in$-$house $($at a cost of $$10$ Million$),$ in which case there is an additional uncertainty about the demand for the technology. If the demand is high $($p $=0\mathrm{.}25),$ the company would make $$55$ Million in revenues, if the demand is medium $($p $=0\mathrm{.}55)$ the company would make $$33$ Million and if the demand is low $($p $=0\mathrm{.}20)$ the company would still make $$15$ Million.$$Draw and solve a decision tree for this situation, assuming that the decision maker is risk neutral. Should the company continue the development of the technology and, if it does, should it license it or produce it in$-$house in case a patent is awarded?