Question

A mail-order house uses 16,870 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Number of Boxes Price per Box 1,000 to 1,999 $1.25 2,000 to 4,999 1.20 5,000 to 9,999 1.15 10,000 or more 1.10 a. Determine the optimal order quantity. (Round your answer to the nearest whole number.) Optimal order quantity boxes b. Determine the number of orders per year. (Round your answer to 2 decimal places.) Number of order per year

Answer 1

Answer and Explanation:

a. The optimal order quantity or economic order quantity is shown below:

$= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}$

$= \sqrt{\frac{2\times \text{16,870}\times \text{\ 96}}{\text{\ 0.60}}}$

= 2,323.45 units

b. And, the number of orders per year is

= Annual demand ÷ Economic order quantity

= 16,870 boxes ÷ 2,323.45 units

= 7.26 orders per year

We simply applied the above formulas to find out the optimal order quantity and the number of orders per year