After evaluating the effectiveness of her initial inventory model, Jane Brewster realized she needed

to address the leftover coffee beans. The shop can purchase coffee beans at $$10$ per kilogram and

sell any surplus within two weeks at $$12$ per kilogram. Any unsold beans are used for

complimentary samples.

$($a$)$ What type of inventory model should Jane use for managing leftover coffee

beans?

$($b$)$ Given the ability to sell surplus beans, what is the optimal service level that Jane

should target?

$($c$)$ Assuming the demand for coffee beans follows a normal distribution with a

mean of $7\mathrm{.}5$ kilograms$/$day and a standard deviation of $1,$ calculate the optimal inventory

level of coffee beans Jane should maintain.

$($d$)$ In $2024,$ Jane Brewster partners with a local compost company willing to buy

unused coffee beans for $$2$ per kilogram to promote sustainability. What would be the new

optimal inventory level of coffee beans?

$($e$)$ Discuss one positive and one negative aspect of the buy$-$back policy with the

compost company.

$($f$)$ With increasing coffee sales, Jane decides to reduce the stockout risk to less than

$2\%.$ As a consultant, how would you advise adjusting the buy$-$back price offered by the compost company to maintain this low stockout risk?