$4\mathrm{.}7$ The actual demand for the patients at Omaha Emergency Medical Clinic for the first $6$ weeks of this year follows:

$\backslash$table$[[$WEEK$,\backslash$table$[[$ACTUAL NO$.$ OF$],[$PATIENTS$]]],[1,65],[2,62],[3,70],[4,48],[5,63],[6,52]]$

Clinic administrator Marc Schniederjans 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 $0\mathrm{.}333$ on 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$)$ What if the weights were $0\mathrm{.}40,0\mathrm{.}30,0\mathrm{.}20,$ and $0\mathrm{.}10,$ respectively? Now what is the forecast for week $7?{?}_a$