Answer:
Economic order quantity = 34.64 cars per order ≈ 35 cars per order.
Total Annual Cost = $29,215.7
Step-by-step explanation:
We will use the following variables:
Q = Quantity being ordered
Q* = the economic order Quantity: the result being sought
D = annual Demand for the item, over the year = 40 × 12 = 480
P = unit Production cost = $60
S = Ordering Cost regardless of the number of units in the order (fixed cost per production order) = $15 per order
H = annual cost to Hold one unit = 20% of $60 = $12
It is important to note which variables are annualized, which are per-order and which are per-unit.
Using the variables, here are the components of the first equation
Total Annual Cost, TC = PC + SC + HC
PC = P x D
Production Cost = (unit Production cost) × (the annual Demand)
SC = (D x S)/Q
Ordering Cost = (annual Demand) × (cost per production setup) / (the order Quantity)
HC = (H x Q)/2
Holding Cost = (annual unit Holding cost) × (order Quantity) / 2 (because throughout the year, on average the warehouse is half full).
So TC = PC + SC + HC = (P x D) + ((D x S)/Q) + ((H x Q)/2) = PD + (DS/Q) + HQ/2
To obtain the optimal order quantity, Q* that minimizes TC, at the minimum TC, dTC/dQ = 0
dTC/dQ = (H/2) – (D x S)/(Q²) = 0
(H/2) – (D x S)/(Q²) = 0
Solving for Q, which is Q* at this point.
(Q*)² = 2DS/H
Q* = √(2DS/H)
a) Economic order quantity
Q* = √(2DS/H)
D = 480 cars
S = $15
H = $12
Q* = √(2×480×15/12) = 34.64 cars per order ≈ 35 cars per order.
b) Total Annual Cost with no backorders
TC = PC + SC + HC = (P x D) + [(D x S)/Q] + [(H x Q)/2]
P = $60
D = 480
S = $15
H = $12
Q = 34.64 cars per order (Using the exact value obtained)
Q = 35 cars per order (Using the realistic approximation for the quantity of cars per order)
Total Annual Cost using the exact value for quantity of cars per order obtained.
= (60 × 480) + [(480 × 15)/34.64] + [(12×34.64)/2]
= 28,800 + 207.85 + 207.84 = $29,215.69
Total Annual Cost Using the realistic quantity of cars per order
= (60 × 480) + [(480 × 15)/35] + [(12×35)/2]
= 28,800 + 205.71 + 210 = $29,215.71
Hope this Helps!!!
