Qwerty Corp. is about to begin production on two homes in a new housing subdivis
ID: 385928 • Letter: Q
Question
Qwerty Corp. is about to begin production on two homes in a new housing subdivision. Qwerty Corp. anticipates that it will need 80,000 square feet of lumber over its 450 day construction cycle. Ordering and holding costs are $6/order and $8/sq.ft., respectively. Qwerty Corp.'s turnaround time on a lumber order is 2 days.
Round intermediate calculations, but round final answer to 2 decimal places.
Part 1. How many orders should Qwerty Corp. make to minimize inventory costs?
Part 2. At what inventory level should Qwerty Corp. order lumber if the company wants to minimize inventory costs?
Part 3. What is the total cost per inventory order for Qwerty Corp.?
Part 4. How many units of lumber will Qwerty Corp. have in its inventory at the end of the 3rd day of construction?
Explanation / Answer
Following are the relevant details :
Demand over construction cycle = D = 80,000 square feet
Ordering cost = Co = $6 / order
Unit holding cost = Ch = $8
The economic order quantity ( EOQ ) which minimizes total inventory cost
= Square root ( 2 x Co x D/ Ch )
= Square root ( 2 x 6 x 80,000/ 8 )
= 346.41 square feet
= 80,000 / 346.41
= 230.94
= ( 80,000/ 450 ) x 2
= 355.55 square feet
= Average inventory x Unit holding cost
= EOQ/2 x Ch
= 346.41/2x 8
= $1385.64
Total ordering cost during construction cycle
= Ordering cost per order x Number of orders
= $6 x 230.94
= $1385.64
Total inventory cost
= Total holding cost + Total ordering cost
= $1385.64 + $1385.64
= $2771.28
Total cost per inventory order
= Total inventory cost / Number of orders
= $2771.28 / 230.94
= $12
We assume that quantum of stock at day ZERO = 0
Order quantity of EOQ which is 346.41 square feet is ordered and it takes 2 days to reach since turnaround time on a lumber order is 2 days.
Therefore , quantum of inventory at the end of 2 days = 346.41
Daily consumption of lumber = 80,000 square feet / 450 days =177.78 square feet
Therefore ,
Quantum of inventory at the end of 3rd day of construction
= Quantum of inventory at the end of 2 days – Daily consumption of lumber
= 346.41 – 177.78
= 168.63 square feet
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