Q$.4$ Set. $($A$)($a$)$ A firm cleans chemical tank cars in the Bay St$.$ Louis area. With standard equipment, the firm typically cleaned $70$ chemical tank cars per month. They utilized $10$ gallons of solvent, and two employees worked $20$ days per month, $8$ hours a day. The company decided to switch to a larger cleaning machine. Last April, they cleaned $60tank$ cars in only $15$ days. They utilized $12$ gallons of solvent, and the two employees worked $6$ hours a day.

$($i$)$ What was their productivity with the standard equipment?

$[3$ Marks$]$

$($ii$)$ What is their productivity with the larger machine?

$($iii$)$ What is the change in productivity?

$($b$)$ Distinguish between a moving average model and an exponential smoothing model.

$[2$ Marks$]$

$($c$)$ Exponential smoothing is a weighted moving average model wherein previous values are weighted in a specific manner$--$in particular, all previous values are weighted with a set of weights that decline exponentially.

$[2$ Marks$]$