A machine shop uses 2,800 brackets during the course of the year. These brackets were purchased from a supplier 90 miles away. The cost of holding a bracket in inventory for a year is $1. 75. The cost per order is $18. 75. The machine shop operates for 250 days per year
To find the economic order quantity (EOQ), we can use the formula:
EOQ = √((2DS)/H)
where:
D = demand per year = 2,800 brackets
S = cost per order = $18.75
H = holding cost per year per bracket = $1.75
First, let's calculate the Total Annual Cost (TAC):
TAC = (DS/H) + (SH/2) + (Q * S/N)
where:
Q = quantity ordered per order
N = number of orders per year
Since we don't know the values of Q and N, let's use EOQ to determine these values.
EOQ = √((2DS)/H)
EOQ = √((2 * 2,800 * 18.75)/1.75)
EOQ ≈ 215.12 brackets
Now, we can calculate the number of orders per year (N):
N = D/Q
N = 2,800/215.12
N ≈ 13 orders
And the quantity ordered per order (Q):
Q = D/N
Q = 2,800/13
Q ≈ 215.38 brackets
Now that we have Q and N, we can calculate TAC:
TAC = (DS/H) + (SH/2) + (Q * S/N)
TAC = (2,800 * 18.75/1.75) + (1.75 * 215.12/2) + (215.38 * 18.75/13)
TAC ≈ $2,349.31
Therefore, the economic order quantity (EOQ) for the machine shop is approximately 215 brackets per order, and the total annual cost (TAC) is approximately $2,349.31.
To calculate the economic order quantity (EOQ) for the brackets, you can use the following formula:
EOQ = √((2DS) / H)
Where:
D = Demand for brackets per year
S = Cost per order
H = Holding cost per bracket per year
1. Calculate the Demand for brackets per year:
D = Total brackets used per year = 2,800
2. Calculate the Cost per order:
S = $18.75
3. Calculate the Holding cost per bracket per year:
H = $1.75
4. Calculate the Economic Order Quantity (EOQ):
EOQ = √((2 * D * S) / H)
EOQ = √((2 * 2800 * 18.75) / 1.75)
5. Calculate the number of orders per year:
Number of orders = D / EOQ
6. Calculate the time between orders:
Time between orders = Number of working days in a year / Number of orders
Let's calculate the values step by step:
4. Calculate the EOQ:
EOQ = √((2 * 2800 * 18.75) / 1.75)
EOQ = √((2 * 52500) / 1.75)
EOQ = √(105000 / 1.75)
EOQ = √60000
EOQ ≈ 244.948
5. Calculate the number of orders per year:
Number of orders = 2800 / 244.948
Number of orders ≈ 11.426
6. Calculate the time between orders:
Time between orders = 250 / 11.426
Time between orders ≈ 21.9 days
Therefore, the economic order quantity for the brackets is approximately 244.948 brackets per order, and the machine shop should place orders every 21.9 days.