Mountain Aquaculture and Producers Association $($MA&PA$)$ is a small trout producers' cooperative in West Virginia. I Its main product is boned, head$-$removed trout sold to local stores. One of the problems MA&PA is facing is that the demand for its products is seasonal $($see the sales in pounds of boned, head$-$removed trout from Q$11997$ to Q$32000$ below$).$ The manager would like to plan production better.

Lo$5$

Year

$1997$

$1998$

$1999$

$2000$

$01$

$664$

$422$

$803$

$698$

Q$2$

$1,338$

$1,098$

$1,430$

$1,076$

$03$

$1,170$

$1,939$

$1,206$

$1,149$

$04$

$1,069$

$843$

$724$

a$.$ Compute the seasonal relative for each quarter using the centred moving average method.

b$.$ Deseasonalize the data, fit an appropriate model to the deseasonalized data, extend the model four quarters, and reseasonalize these in order to forecast the sales of boned, head$-$removed trout from the fourth quarter of $2000$ to third quarter of $200$lste