If n=48

Average daily demand(d) = 10+n units = 10+48 = 58 units

Number of days in a year = 250 days

Annual demand (D) = 58 units x 250 = 14500 units

Ordering cost (S) = $200+$n = $200+$48 = $248 per order

Holding cost (H) = $0.12 per unit per day

Purchase cost (p) = $15 per unit

Lead time (L) = 4 days

A) If the order quantity (Q) = 600,

Total annual inventory cost = Ordering cost + Holding cost + purchase cost

= [(D/Q) S] + [(Q /2)H] + (pxD)

= [(14500/600)248] + [(600/2)0.12] + (15 x 14500)

= $5993.3333 + $36 + $217500

= $223529.3333

Total daily inventory cost = Total annual inventory cost / number of days in a year

= $223529.3333/250 days

= $894.1173 per day

B) Economic order quantity (Q*) = sqrt of (2DS /H)

= sqrt of [(2 x 14500 x 248) / 0.12]

= 7741.6622 or rounded to 7742 units

C) With economic order quantity (Q*) = 7742 units,

Total annual inventory cost = Ordering cost + Holding cost + purchase cost

= [(D /Q*) S] + [(Q*/2)H] + (pxD)

= [(14500/7742)248] + [(7742/2)0.12] + (15×14500)

= $464.4795 + $464.52 + $217500

= $218428. 9995

D) Reorder point = d x L = 58 x 4 = 232 units

E) length of order cycle = (Q*/D) number of days per year

= (7742/14500)250

= 133.4828 or rounded to 133 days

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