$6-28$ Ross White $($see Problem $6-27)$ wants to reconsider his decision of buying the brackets and is considering making the brackets in$-$house. He has determined that setup cost would be $$25$ in machinist time and lost production time and that $50$ brackets could be produced in a day once the machine has been set up$.$ Ross estimates that the cost $($including labor time and materials$)$ of producing one bracket would be $$14\mathrm{.}80.$ The holding cost would be $10\%$ of this cost.

What is the daily demand rate? $=2500/250=10$

What is the optimal production quantity? EOQ $=(2$ x $2500$ x $25)/$ $$1\mathrm{.}48$ x $(1-10/50)=324\mathrm{.}922$ or $325$ brackets

How long will it take to produce the optimal quantity? $325/50=6\mathrm{.}5$ days

How much inventory is sold during this time? $325/50$ X $10=65$ brackets

If Ross uses the optimal production quantity, what would be the maximum inventory level? $324\mathrm{.}92$ x $0\mathrm{.}8=259\mathrm{.}94$ What would be the average inventory level? $259\mathrm{.}94/2=129\mathrm{.}97$ What is the annual holding cost? $129\mathrm{.}97$ x $1\mathrm{.}48=192\mathrm{.}35$

How many production runs would there be each year? $2500/324\mathrm{.}92=7\mathrm{.}694$ or $8$ production runs$/$year What would be the annual setup cost? $2500/324\mathrm{.}92$ x$25=192\mathrm{.}35$

Given the optimal production run size, what is the total annual inventory cost? $192\mathrm{.}35$ x $194\mathrm{.}35=37384\mathrm{.}71$

If the lead time is one$-$half day, what is the ROP? $2500/250$ x $0\mathrm{.}5=5$