Final answer:
The best order quantity for the eyeglass retailer is found by comparing the total costs at various quantities considering the supplier's discount, and using the Economic Order Quantity (EOQ) model to account for ordering and carrying costs.
Step-by-step explanation:
To determine the best order quantity for the eyeglass retailer, we need to consider the ordering cost, the carrying cost, and the discount offered. Given that the lenses cost $100 each, the retailer orders 250 pairs annually, and the ordering cost is $36, we can use the Economic Order Quantity (EOQ) model to calculate the optimal order size. However, the supplier offers a 10% discount on orders of 50 or more lens pairs, which must also be incorporated into our calculations.
First, we need to find the EOQ without considering the discount using the formula:
EOQ = √((2 * Demand * Ordering Cost) / Carrying Cost Rate)
Carrying cost per lens pair is 20% of $100, which is $20. Thus the EOQ formula becomes:
EOQ = √((2 * 250 * $36) / $20)
However, to find the best order quantity that incorporates the discount, we must ascertain if ordering in multiples of 50 (the minimum quantity for a discount) results in a lower total cost than the calculated EOQ.
The total cost, including the discount, ordering, and carrying costs, needs to be compared at different order quantities: 50, 100, 150, 200, and the EOQ (if it is not one of these quantities).
Ultimately, the best order quantity is the one that results in the lowest total cost.