PROBLEM $3$: DEMAND FORECASTING FOR SPC $(5$ HOURS, $50$ POINTS$)$ Use the structured systematic problem solving approach on this problem, and make sure to provide clear reasoning and explanations to support "everything" you do$.$ Depending on the number of smoothing constants in your forecasting method use one or all of the following smoothing constants: alpha$=0\mathrm{.}06,$ beta$=0\mathrm{.}06,$ gamma$=0\mathrm{.}06.$ First, form a hypothesis $($conjecture$)$ as to which forecasting method Julie Williams should use for black plastic, and be sure to explain the basis $($rationale$)$ for your hypothesis. Then, test your hypothesis by implementing all five forecasting techniques that you've learned. Which technique should Julie Williams use for forecasting the demand for black plastic based on the results of your implementation of the five forecasting techniques? Was your hypothesis correct? What is the demand forecast for black plastic for each of the four quarters of the year $2007?$ What is the annual demand for the year $(2007)$ You will need this information for the next task below. $($Caution: you must work with black plastic demand data ONLY$)$ Extra Credit $(2$ HOURS, $10$ POINTS$)$: What values should Julie use for the smoothing constants $($i$.$e$.,$ alpha, beta, and gamma$)$ of the selected forecasting method$($s$)$ in order to minimize forecast error? TABLE $7-4$ Year $200220032004$ Quarterly Historical Demand for Clear and Black Plastic Demand Quarter $(\text{'}000$ lb$)2,2501,737$ III $2,4127,2693,5142,1433,4597,0564,1202,7662,5568,2535,4914,3824,31512,0355,6483,6964,843$ IV $13,09720052006$