Question

Problem 10A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 280 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The coffeehouse estimates that it costs $45 in paperwork and labor to place an order for the coffee, and holding costs are based on a 20 percent annual interest rate.a)Determine the optimal order quantity for Colombian coffee.b)What is the time between placement of orders?c)What is the average annual cost of holding and setup due to this item?d)If replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory.

Answer 1

The computations are shown below:

Step-by-step explanation:

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

`= \sqrt{\frac{2* \text{Annual demand}* \text{Ordering cost}}{\text{Carrying cost}}}`

`= \sqrt{\frac{2* \text{280}* \text{\$45}}{\text{\$0.48}}}`

= 229 units

The carrying cost is come from

= $2.40 × 20%

b. Time between placement of orders is

= Economic order quantity ÷Annual demand

= 229 ÷ 280

= 0.8179 years

So,

= 0.8179 × 365 days

= 298.53 days

We assume 365 days in a year

c. The average annual cost of ordering cost and carrying cost equals to

= Holding cost + ordering cost

= (Economic order quantity ÷ 2 × Holding cost) + (Annual demand ÷ Economic order quantity × ordering cost)

= (229 units ÷ 2 × $0.48) + (280 ÷ 229 units × $45)

= $54.96 + $55.02

= $109.98

d) Now the reorder level is

= Demand × lead time + safety stock

where, Demand equal to

= Expected demand ÷ total number of weeks in a year

= 280 pounds ÷ 52 weeks

= 5.38461

So, the reorder point would be

= 5.38461 × 3 + $0

= 16.15 pounds