Q$\mathrm{.}2$ Set. $($A$)$ The actual demand for the patients at Omaha Emergency Medical Clinic for the first $6$ weeks of this year follows:

Clinic administrator wants you to forecast patient demand at the clinic for week $7$ by using this data. You decide to use a weighted moving average method to find this forecast. Your method uses four actual demand levels, with weights of $0\mathrm{.}333$ in the present period, $0\mathrm{.}25$ one period ago, $0\mathrm{.}25$ two periods ago, and $0\mathrm{.}167$ three periods ago.

a$)$ What is the value of your forecast?

b$)$ If instead, the weights were $20,15,15,$ and $10,$ respectively, how would the forecast change? Explain why.

c$)$ Calculate the MAPE for both cases.