Question: $4$

$($a$)-.$ An industrial distributor purchase $9,000$ boxes monthly $0$ transport goous,

Assume $300$ working days$/$year$.$ The information availabie for some of costs elemem.

are given as: Unit $($box$)$ price $=$$$12\mathrm{.}5$ unit, $-$ Ordering cost $=8,750$ lorder

Inventory holding cost $=2\mathrm{.}5\%$ of the unit price $/$month

Interest rate including Insurance $18\%$ compounded annually.

Calculate: $(1-)$The optimum order quantity and Draw the inventory model,

$2-$ The optimum number of orders per year and the cycle time,

$3-$ The minimum total annual inventory cost,

$4-$ The reorder point if the lead time is $12$ days.

$($b$)-$ Determine the break$-$even points for the three alternatives shown in the ne table.

How you can choose the preferabl one by using two methods:

$(1)$ Mathematical solution, and$(2-$Graphical Solution.

$\backslash$table$[[$Alternative$,$Centre Lathe,Turret Lathe,Automatic Lathe$],[$Depreciation $($S$/$year$),60{10}^3,220{10}^3,530{10}^3$