$(20$ marks$)$ Bart's Bakery sells a low$-$fat multigrain loaf. Bart wants to try a new supplier for multigrain flour and yeast but wants to be sure that the loaves don't change. Before he changes, he weighs five loaves a day for four consecutive days. $(20$ marks$)$ The data are below.

$\backslash$table$[[,$Loaf $($grams$),,,,],[$Day$,1,2,3,4,5],[1,409,413,395,387,404],[2,412,396,389,401,412],[3,392,387,388,415,406],[4,397,412,404,386,411]]$

a$)$ Establish upper and lower control limits for the bread baking process..

Operations Management, FARE$*3310-$ Winter $25$: Assignment $1$

b$)$ Is the baking process currently under control?

c$)$ Bart makes $5$ loaves with the new flour and yeast $($taking a new sample$).$ They weigh $402,418,399,421$ and $419.$ Do the new ingredients produce loaves that are within the acceptable control limits of the chart you developed? $(5$ marks$)$