$1.$ Based on the information shown below, develop forecasts for April to October using:

$($a$)$ A $3-$period weighted moving average model $($w$1=0\mathrm{.}5,$ w$2=0\mathrm{.}3,$ and w$3=0\mathrm{.}2).$

$($b$)$ An exponential smoothing model with $\backslash$alpha $=0\mathrm{.}35.$ Assume the forecast for March was $950.$

Month Actual Demand

Jan $1050$

Feb $975$

Mar $1000$

Apr $870$

May $970$

Jun $1220$

Jul $1170$

Aug $1150$

Sep $1235$

Oct $1275$

$2.$ Based on the information shown below, calculate MAD, MSE and tracking signal.

Week Actual Demand Forecast

$1750770$

$2690730$

$3820710$

$4850790$

$5870840$

$6780850$

$7915890$

$8950920$

$3.$ For the information given, rank the customers in terms of customer lifetime value.

Avg. Annual Sales Avg. Profit Margin Expected Lifetime

Customer $1$: $$3,45017\%8$ years

Customer $2$: $$2,00013\%6$ years

Customer $3$: $$1,40032\%10$ years

Use a discount rate of $6$ percent and treat the average sales figures as annuities. Should any of these customers be fired?