Business ScenarioTBay Woods Co$.$ is a manufacturer for wood products in Northwestern Ontario. Due to themarket and technology changes, the company is considering to further develop its business withthe following three options: Option $1$: to acquire another factory for wood processing, which would invest $$80,000$; Option $2$: to upgrade the current assembly line, which would cost $$50,000$; Option $3$: to keep the current settings no change, i$.$e$.,$ no new costs and no new revenue.Based on the historical data, the company also considers three possible market conditions in thenear future: High demand market: where the newly built factory can generate $$120,000$ revenue, andthe upgrades can generate $$80,000$ revenue. Low demand market: where the new factory can only generate $$60,000$ revenue, and theupgrades can generate $$40,000$ revenue. No change in market demand: where the new factory can generate $$85,000$ revenue, andthe upgrades can generate $$60,000$ revenue.You are a new hire at the company, and the manager asks you to analyze the situations and makerecommendations for decision$-$making. Assume the capacity would meet the market demand inall situations, with the same price at $$10/$unit and the same cost at $$5/$unit$\mathrm{.}1.$ Formulate the problem for decision analysis. Show the decision alternatives and states ofnature, and develop a payoff table with the outcomes $($i$.$e$.,$ profit$)\mathrm{.}2.$ Considering this is a decision$-$making problem under uncertainty, apply the threestrategies to analyze the problem and come up your recommendation for each strategy$\mathrm{.}3.$ Assume that a recent market research report predicts the market conditions with $40\%$chance of high demand, $25\%$ of low demand, and $35\%$ of no change. Would you changeyour recommendations? Why?$4.$ Calculate the expected value of perfect information $($EVPI$)\mathrm{.}5.$ Create a decision tree with the business scenario and the information from $(3.)$ to analyzethe problem and verify your recommendations.