Q$6$: Primo's Inventory Management

$(8$ Marks$)$

If you knew that Primo's has many units stored in their own inventory to prepare for their operations as presented in the following table:

$\backslash$table$[[$Item$,1,2,3,4,5,6,7,8,9,10],[$Quantity$,1,400,4,800,300,120,7,600,8,000,12,000,600,60,5,800],[$Price$,375,225,750,1375,100,50,15,25,600,3]]$

Required:

Perform the ABC analysis for Primo's Inventory

$(3$ Marks$)$

If Primo's Juice Factory is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of $200$ units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, $50$ weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of LE $300.$ Inventory holding costs will be LE $10$ a year.

As a production manager of Primo's Juice Factory:

a$.$ Which inventory model should be used here: the basic EOQ, the EPQ, or the single period model? How do you know?

$(0\mathrm{.}5$ Mark$)$

b$.$ What run quantity should be used to minimize total annual costs?

$(1$ Mark$)$

c$.$ Calculate the Total Inventory Cost for this case.

$(1$ Mark$)$

d$.$ What is the length of a production run in days?

$(0\mathrm{.}5$ Mark$)$

e$.$ During production, at what rate will inventory build$-$up$?$

$(0\mathrm{.}5$ Mark$)$

f$.$ If the manager wants to run another job between the runs of this item, and needs a minimum of $10$ days per cycle for the other work, will there be enough time?

$(1\mathrm{.}5$ Mark$)$