Consider a basic economic order quantity (EOQ) model with the following characte

ID: 3319691 • Letter: C

Question

Consider a basic economic order quantity (EOQ) model with the following characteristics:

Item cost: $15.

Item selling price: $20.

Monthly demand: 500 units (constant)

Annual holding cost: 9% of purchase cost

Cost per order: $18.

Order lead time: 5 days

Firm's work year: 300 days (50 weeks @ 6 days per week)

Safety stock: 15% of monthly demand

For this problem, determine the values of:

A. Q* the optimal order quantity.

B. R, the reorder point.

C. T, the cycle time.

D. M, the maximum quantity in inventory. (the answer is: 475 but I need to know the steps)

E. Total annual inventory cost.

Item cost (CP): $15.

Item selling price (SP): $20.

Monthly demand: 500 units (constant)

Annual holding cost: 9% of purchase cost

Cost per order (O) : $18.

Order lead time (L): 5 days

Firm's work year:300 days (50 weeks @ 6 days per week)

Annual Demand (D) = 500*12 = 6000

Annual Holding Cost (H) = $15*9% = $1.35

A. Q* the optimal order quantity.

Using EOQ model,

Q* = (2*6000*18/1.350)^0.5 = 400 units

B. R, the reorder point.

R = L*D/300 = 5*6000/300 = 100 units

C. T, the cycle time.

T = (Q*)/(D*300) = 400/6000*300 = 20 days

D. Total annual inventory cost (TC)

TC = Holding Cost (HC) + Ordering Cost (OC) = (Q*)/2*H + D/(Q*)*O = 270 + 270 = 540

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