Question

A manufacturer requires 1,000 units of a raw material per month. The ordering cost
is 15 per order. The carrying cost in addition to *2 per unit is estimated to be
15% of the average inventory per unit per year. The purchase price of the raw
material is 10 per unit. Find the economic lot size and the total cost. The
manufacturer is offered a 5% discount in purchase price for orders of 2,000 units or
more but iess than 5,000 units. A further 2% discount is available for orders of
5,000 units or more units. Which of the three ways of purchase he should adopt ?
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Answer 1

The manufacturer should adopt the option that results in the lowest total cost.

The economic lot size can be determined using the economic order quantity (EOQ) formula, which balances the cost of ordering and carrying inventory.

The formula for EOQ is:

EOQ = $\sqrt(2DS/H)$

where D = demand (1,000 units per month),

S = ordering cost (15 per order),

and H = carrying cost (15% of average inventory value per year).

The average inventory value can be calculated as (EOQ/2) and the carrying cost can be estimated as

$(H * (EOQ/2) * (10 per unit)).$

The total cost of ordering and carrying inventory can be calculated as (EOQ/2) × S + (EOQ/2) × H × (10 per unit).

If the manufacturer purchases 1,000 units, the total cost will be

(1,000/2) × 15 + (1,000/2) × 15% × (10 per unit) × (1,000/2).

If the manufacturer purchases 2,000 units, the purchase price will be 9.5 per unit and the total cost will be

(2,000/2) × 15 + (2,000/2) × 15% × (9.5 per unit) * (2,000/2).

If the manufacturer purchases 5,000 units, the purchase price will be 9 per unit and the total cost will be

(5,000/2) × 15 + (5,000/2) × 15% × (9 per unit) × (5,000/2).

The manufacturer should adopt the option that results in the lowest total cost.

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