Techware Incorporated is considering introducing two new software products to the market. The company has four options regarding these products: introduce neither product, introduce product $1$ only, introduce product $2$ only, or introduce both products. Research and development costs for products $1$ and $2$ are $$180,000$ and $$160,000,$ respectively. Note that the first option entails no costs because research and development efforts have not yet begun. The success of these software products depends on the national economy in the coming year. The company's revenues, depending on its decision and the state of the economy, are below. The probabilities of a strong, fair, or weak economy in the coming year are assessed as $0\mathrm{.}10,0\mathrm{.}50,$ and $0,40,$ respectively.Trend in the national economyDecisionsIntroduce neither productIntroduce Product $1$ onlyIntroduce Product $2$ onlyIntroduce both productsa$)$ Construct a decision tree to help Techware to make the decision. State all decisions, states of nature with their probabilities, and outcomes on the tree.StrongFairWeakSOSOSO$$500,000$$$260,000$$$120,000$$$430,000$$$230,000$$$110,000$$$880,000$$$390,000$$$200,000$suppose that the Techware decision process is risk neutral, i$.$e$.,$ uses the expected monetary value $($EMV$)$ criterion. Find the decision that maximizes their EMV.