Question 1 Stochastic Optimization. 30 Pts A small company producing four types of fedora hats (Raw edge, folded edge, ribbon edge, and Cavanagh edge) would like to determine how much of each type to produce for the next quarter. They can purchase at most 650 yards of wool yarn before the start of the quarter from their local supplier. The company has a heritage of using only the local supplier who raises sheep with the best quality wool. The raw edge hats take the least amount of time and labor to produce, and the company can produce 650 of the folded edge hats from the 650 yards of wool yarn (1yard per raw edge hat) they can purchase. \begin{tabular}{|l|l|l|l|l|l|}\hline \multirow{2}{*}{Hat Demand Intensity} & \multirow[t]{2}{*}{Probability} & \multicolumn{4}{|c|}{Demand for Each Type of hat}\\\hline & & Cavanagh & Ribbon & Folded & Raw Edge \\\hline High & 45\% & 60 & 180 & 250 & 360\\\hline Medium & 30\% & 45 & 140 & 190 & 280\\\hline Low & 25\% & 28 & 100 & 140 & 250\\\hline \multicolumn{6}{|c|}{Profits, Materials, and costs used for each Type of Hat}\\\hline & & Cavanagh & Ribbon & Folded & Raw Edge \\\hline & Revenue/hat & \$ 60 & \$ 45 & \$ 35 & \$ 25\\\hline & Yard of Yarn Used/hat & 2 & 1.6 & 1.2 & 1\\\hline \multicolumn{2}{|c|}{Production cost compared to raw edge} & 2.5 & 2 & 1.5 & 1\\\hline \end{tabular} Historical demand for the hats obeys the distribution shown in Table 1. Use a two-stage stochastic optimization model to determine how many hats of each type the Company should produce to maximize its expected revenue 2. solve the problem in Excel and also 3. provide the mathematical model.