Question

The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 35,000 yards of denim per year to make jeans. The cost of ordering denim from the textile company is $500 per order. It costs Western $.35 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.

Answer 1

Answer and Explanation:

a. The computation of the economic order quantity is shown below:

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

$= \sqrt{\frac{2\times \text{35,000}\times \text{\ 500}}{\text{\ 0.35}}}$

= 10,000 yards

b.. The total cost of ordering cost and carrying cost equals to

= Annual ordering cost + Annual carrying cost

= Annual demand ÷ Economic order quantity × ordering cost per order + Economic order quantity ÷ 2 × carrying cost per unit  

= 35,000 ÷ 10,000 × $500 + 10,000 ÷ 2 × $0.35

= $1,750 + $1,750

= $3,500

c. Optimal No. of Orders is

= Annual Demand ÷Order Quantity

= 35,000 ÷ 10,000

= 3.5

Time between two orders is

= No. of Working Days ÷ No. of orders

= 365 ÷ 3.5

= 104 days

We assume there is a 365 days in a year and we applied the above formulas