Answer:
a) Inventory cost = 12r + 4x
b) Constraint
r = (D/x) = (4800/x)
c) Optimal order quantity = x = 120
Minimum Inventory Cost = C = $960
Optimal number of orders in a year = r = 40
Step-by-step explanation:
x be the order quantity and r the number of orders placed during the year.
We will use the following variables:
x = Quantity being ordered per run
D = annual Demand for the item, over the year = 4800
O = ordering cost, regardless of the number of units in the order (fixed cost per order) = $12
H = annual cost to Hold/carry one unit = $8
r = the number of orders placed during the year
It is important to note which variables are annualized, which are per-order and which are per-unit.
Inventory cost = Ordering Cost + Holding or Carrying Cost
Ordering cost = (ordering cost per order) × (number of orders) = 12r
Holding Cost = (annual unit Holding cost × order Quantity)/2 (because throughout the year, on average the warehouse is half full).
Holding cost = (8 × x)/2 = 4x
Inventory cost = 12r + 4x
b) The constraint equation
Total demand = (order quantity per order) × (number of orders)
D = rx
r = (D/x)
r = (4800/x)
c) Inventory Cost = C = 4x + 12r = 8x + 12(4800)/x
C = 4x + 57600/x
At minimum inventory cost, (dC/dx) = 0
(dC/dx) = 4 - 57600/x² = 0
57600 = 4x²
x² = (57600/4)
x² = 14400
x = √14400
x = 120
C = 4x + 57600/x
C = 4(120) + (57600/120)
C = 480 + 480 = $960
Hope this Helps!!!
