Question

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

Answer 1

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.