$($Complete using Excel spreadsheet and show each formula used and step by step process$).$ It is also important to show all the numbers used, don't just explain the process, please show working steps.

Dr$.$ Chris is a chiropractor and treats patients from her home office. The following data

represent the number of patients that Dr$.$ Chris treated over the past six days.

a$.$ Calculate the patient forecast for Day $7$ using a three$-$period moving average.

b$.$ Calculate the patient forecast for Day $7$ using a three$-$period weighted moving average with

weights $0\mathrm{.}5,0\mathrm{.}3,$ and $0\mathrm{.}2$ applied from most current to oldest day respectively.

c$.$ Find the optimal weights. $($ explain what this is$,$ and how to calculate it step by step$)$

d$.$ Calculate the patient forecast for Day $7$ using a simple exponential model with smoothing

constant of $0\mathrm{.}5.$

e$.$ Find the optimal smoothing constant.

f$.$ Evaluate all models using the MSE and MAPE. Which model is the best model?