After assessing the model used in part $1,$ Ann Chovies, found out that he is missing the assessment of pepperoni leftovers. In fact, they can purchase the pepperoni from a distributor for $$3$ per pound and sell it within a week $($before the expiry date$)$ for $$4$ per pound. Ann Chovies and her staff eat any pepperoni leftovers.

$($a$)(2$ points$)$ Which type of inventory model should we use?

$($b$)(2$ points$)$ In th$$se conditions, what is the optimal service level that Ann Chovies should target?

$($c$)(2$ points$)$ Assuming that, as mentioned above, demand for pepperoni follows a normal distribution with a mean of $19$ pounds$/$day and a standard deviation of $2,$ what is the optimal pepperoni weight $($in pounds$)$ that Ann Chovies should stock?

$6$

$($d$)(2$ points$)$ In $2023,$ Ann Chovies discovered that Dr$.$ Nader and her VIP team were working on waste management and they were willing to buy the pepperoni leftovers for $$1$ the pound. Aiming at encouraging the circular economy, Ann Chovies signed a recycling contract with Dr$.$ Nader. What would become the new optimal pepperoni quantity $($in pounds$)$ that Ann Chovies should stock?

$($e$)(2$ points$)$ Name one positive and one negative aspect in terms of the buy$-$back policy?

$($f$)(2$ points$)$ Now that the demand for pepperoni pizzas is considerably increasing, Ann Chovies took the decision to not accept a stockout risk more than $1\%.$ Accordingly, as a consultant, Dr$.$ Nader had to adjust her buy$-$back policy to avoid losing the agreement with Ann Chovies. Would you help her out to identify the new discount price $($i$.$e$.$ salvage$)$ should she offer to Ann Chovies?