Problem $2.$ Use the attached Excel file with the quarterly demand $($in $1000$ s of cases$)$ for a national beer distributor over the past $4$ years $($data taken from textbook problem $11-47).$

Generate a forecast using a $4$ period weighted moving average wMA$(4),$ using weights $1,2,3,4(4$ being applied to the most recent period$).(3$pts$)$

a$.$ What is the forecast for Quarter $)=(17?$

b$.$ Find the MAD based on periods $5$ through $)=(5,6,$dots,$16.$ What is the MAD?

c$.$ Use nonlinear programming to find the weights that minimize MAD.

i$.$ What are the weights?

ii$.$ What is the MAD?

iii. What is the forecast for Quarter $)=(17$ using these weights?