Question

Superior Electric uses 4,000 toggle switches a year. Switches are priced as follows: 1) 1 - 499 for $0.90 each, 500 - 999 for $0.85 each, and 1,000 or more for $0.82 each. It costs approximately $18 to prepare an order and receive it, and carrying costs are 18% of purchase price per unit on an annual basis. Determine the optimum order quantity and the total annual cost.

Answer 1

Answer:

Given = Annual demand = 4,000

Ordering cost = $18 per order

Carrying cost = 18% of purchase price

Let us calculate EOQs for prices given to evaluate which EOQ falls within their respective ranges:

1. EOQ = SQRT (2 * 4000 * 18 / (18% * 0.90)) = 942.81

The price of $0.90 is for range from 1 to 499; since EOQ = 942.81 units, this price is not applicable.

2. EOQ = SQRT (2 * 4000 * 18 / (18% * 0.85)) = 970 units

The price of $0.85 is for range from 500 to 999 and EOQ of 970 falls within this range.

Hence EOQ = 970 Units

Optimum order quantity =970 units

Total cost = = carrying cost + ordering cost + purchasing cost = (970 / 2) * (18%* 0.85) + 18 * (4000 / 970) + 4000 * 0.85

= $3548

Hence:

Optimum order quantity =970 units

Total annual cost = $3,548