Climat Co has been buying a chemical water conditioner for its bait (to help kee
ID: 384769 • Letter: C
Question
Climat Co has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion using EOQ analysis. The supplier has now offered ZZZ a discount based on the quantity purchased (prices and quantity ranges can be found in the table below). Current data for the problem are: D = 200 units per year; S = $20.00, I = 20% per year.
(a) What is the optimal order quantity?
(b) What are the annual total cost, including product cost, of continuing their current behavior?
Range 1
Range 2
Range 3
Quantity
1 – 59
60 – 179
180
Unit Price, P
$5.00
$4.75
$4.50
Range 1
Range 2
Range 3
Quantity
1 – 59
60 – 179
180
Unit Price, P
$5.00
$4.75
$4.50
Explanation / Answer
To be calculated:
a) Optimal Order Quantity
b) Annual Total Cost
Given Information:
Annual Demand = 200 units
Setup cost = $20
Price, P1 (Q = 1-59) = $5
Price, P2 (Q = 60-179) = $4.75
Price, P3 (Q >= 180) = $4.5
Holding cost per unit per year = 20%
H1 = 20% of P1 = 20% of $5 = $1
H2 = 20% of P2 = 20% of $4.75 = $0.95
H3 = 20% of P3 = 20% of $4.5 = $0.9
Solution:
Economic order quantity or Optimal order quantity is calculated as:
Q* = 2 x annual demand x cost per order / holding cost per unit per year
Q1 = 2 x D x S / H1
Q1 = 2 x 200 x 20 / 1
Q1 = 89.44 = 89 units
Q2 = 2 x D x S / H2
Q2 = 2 x 200 x 20 / 0.95
Q2 = 91.76 = 92 units
Q3 = 2 x D x S / H3
Q3 = 2 x 200 x 20 / 0.9
Q3 = 94.28 = 94 units
Annual Total Cost can be calculated as;
TC = (Order Quantity/2) x holding cost per unit per year + (annual demand/order quantity) x Setup cost
All calculated quantities (Q1 = 89, Q2 = 92, Q3 = 94) lie in the range of (Q = 60 - 179), Price per unit = $4.75
Holding Cost for all the three quanities = $0.95
TC1 (Q = 89) = (89/2) x 0.95 + (200/89) x 20 = 42.28 + 44.94 = $87.22
TC2 (Q = 92) = (92/2) x 0.95 + (200/92) x 20 = 43.7 + 43.48 = $87.18
TC3 (Q = 94) = (94/2) x 0.95 + (200/94) x 20 = 44.65 + 42.55 = $87.2
Since, the Annual Total Cost is lowest ($87.18) with order quantity of 92 units, therefore, for Climat Co.
(a) Optimal Order Quantity = 92 units
(b) Annual Total Cost = $87.18
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