EOQ is also known reorder quantity (ROQ).
In EOQ, total cost of holding inventory is minimum and ordering cost is equal or minimum to storage cost of materials.
While determining EOQ, ordering cost and carrying cost should be consider.
Keep In Mind (KIM)
If purchasing quantity increases, carrying or holding cost also increases but ordering cost decreases. 
If purchasing quantity decreases, carrying cost also decreases but ordering cost increases. 
Carrying cost is calculated always on purchase price not on sales price. 
Ordering cost is repurchase cost and is repeated in nature.
Purchase of large quantity of materials helps to reduce ordering cost; it includes:
· Salary of staff related to purchasing, inspection and tour.
· Transportation expenses, transit insurance etc.
· Cost of stationery, postage, telephone, fax etc related to purchasing.
· Cost of paper work as tender, quotation, advertisement etc.
It is also known keeping cost and holding cost.
The carrying cost suggests purchasing small quantity of materials.
If small quantity is purchased, the storage cost will be low.
It is the expenses related to after material purchased; it includes:
· Salary of store keeper and related to holding of materials.
· Rent of godown or warehouse
· Insurance cost of materials
· Interest on capital which is blocked on materials purchased
· Losses due to breakage, spoilage (date expired), obsolescence (old fashioned).
· Desire rate of return from investment in inventory.
· Cost of stationery, postage, telephone, fax, email etc related to holding of materials etc.
Keep in Mind (KIM)
Some important synonyms or abbreviations 
A = annual requirement or need 
O = ordering cost per order, administrative cost per order, procurement cost per order 
C = carrying cost per order, holding cost per order, production cost per order 
P = purchase price per unit, cost per unit 
Q = quantity size or order size 
SQRT = square root or √ 
Assumption to Determine the Economic Order Quantity
Major assumptions of EOQ are given below:
The fixed quantity is ordered at each reordering point.
Time lag in the placement of an order and its delivery, annual demand, carrying cost and ordering are certain.
Purchase price of an item is unaffected by the quantity ordered.
No stock outs occur.
While determining the economic order quantity, the management considers the cost of quality only to the extent that these costs affected ordering costs or carrying costs.
EOQ can be determined in three ways; they are:
1. Mathematical or formula method
2. Trial and error method
3. Graphic method
Here, SQRT means square root
EOQ (in units) 
= SQRT 2AO ÷ C 

EOQ (in order) 
= A ÷ EOQ units 

EOQ (in cost) 
= SQRT 2AOC 



Average period between the orders 
= EOQ units × Days in year ÷ Annual require 

Length of inventory circle 
= Days in year ÷ No. of order 

Or 
= EOQ units ÷ Daily use 



EOQ total cost, there are different methods to find out total cost 

Total cost excluding cost of materials (order size is NOT given) 
= SQRT 2AOC 

Total cost including cost of materials (order size is NOT given) 
= (A×P) + SQRT 2AOC 

Total cost including cost of materials discount (order size is NOT given) 
= (A×P – Discount) + SQRT 2AOC 




Total cost excluding cost of materials (order size is given) 
= (AO ÷ Q) + (QC ÷ 2) 

Total cost excluding cost of materials with discount (order size is given) 
= (AO ÷ Q) + (QC ÷ 2) – Discount 

Total cost including cost of materials (order size is given) 
= (A×P) + (AO ÷ Q) + (QC ÷ 2) 

Total cost including cost of materials with discount policy 
= (A×P – Discount) + (AO ÷ Q) + (QC ÷ 2) 

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2072, Q: 6
The following extracted information are given:
EOQ 4,000 units
Ordering cost per order Rs 160
Carrying cost per unit Rs 2
Required: Annual requirement
[Answer: A = 100,000 units]
SOLUTION:
Here, SQRT means square root
Annual requirement
EOQ 
= SQRT 2AO ÷ C 
4,000 
= SQRT 2 × A × Rs 160 ÷ Rs 2 
4,000 
= SQRT 160A 
(4,000)^{2} 
= SQRT 160A squaring both sides 
16,000,000 
= 160A 
A 
= 16000000 ÷ 160 

= 100,000 units 
2073, Q: 6
The following extracted information of A Manufacturing Company are provided:
Annual requirement 36,000 units
Material cost per unit Rs 20
Carrying cost per unit 10% of inventory value
Ordering cost per order Rs 10
Required: Total cost at EOQ
[Answer: Total cost = Rs 1,200]
SOLUTION:
Carrying cost (C) = Rs 20@10% = Rs 2
SQRT means square root
(a) Total cost at EOQ
= SQRT 2AOC
= SQRT 2 × 36,000 × Rs 10 × Rs 2
= SQRT 14,40,000
= Rs 1,200
2075, Q: 6
A Manufacturing Company provided the following particulars:
Yearly requirement 25,000 units
Purchase price per unit Rs 10
Ordering cost per order Rs 20
Inventory carrying cost 10% of purchase price
Required: Total cost at EOQ
[Answer: Total cost = Rs 1,000]
SOLUTION:
Carrying cost (C) = Rs 10@10% = Re 1
SQRT means square root
(a) Total cost at EOQ
= SQRT 2AOC
= SQRT 2 × 25,000 × Rs 20 × Re 1
= SQRT 10,00,000
= Rs 1,000
2076, Q: 9
The following extracted information are given:
Economic order quantity 3,000 units
Ordering cost per order Rs 200
Carrying cost per unit Rs 1.20
Required: Annual requirement
[Answer: A = 27,000 units]
SOLUTION:
Here, SQRT means square root
Annual requirement
EOQ 
= SQRT 2AO ÷ C 
3,000 
= SQRT 2 × A × Rs 200 ÷ Rs 1.2 
3,000 
= SQRT 333.33A 
(3,000)^{2} 
= SQRT 333.33A squaring both sides 
9,000,000 
= 333.33A 
A 
= 9,000,000 ÷ 333.33 

= 27,000 units 
2077, Q: 6
The following extracted information are given:
Carrying cost per unit Re 0.50
Ordering cost per order Rs 40
Economic order quantity 1,000 units
Required: Annual requirement
[Answer: A = 6,250 units]
SOLUTION:
Here, SQRT means square root
Annual requirement
EOQ 
= SQRT 2AO ÷ C 
1,000 
= SQRT 2 × A × Rs 40 ÷ Re 0.50 
1,000 
= SQRT 160A 
(1,000)^{2} 
= SQRT 160A squaring both sides 
1,000,000 
= 160A 
A 
= 1,000,000 ÷ 160 

= 6,250 units 
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2054/Cancelled, Q: 3
Annual requirement of raw materials as reported were 480,000 kg. Procurement activities to be undertaken required expense of Rs 10,000. Monthly possession cost of raw materials per kg will be Rs 2.
Suggest by applying relevant formulas:
(a) Monthly optimum quantity; (b) No. of procurement to be made during the month
[Answer: (a) EOQ units = 20,000 units; (b) No. of order = 2 times]
SOLUTION:
Given and working note:
A = 480,000 kg
Monthly A = 480,000 ÷ 12 = 40,000
O = Rs 10,000
C = Rs 2
(a) Monthly optimum quantity (EOQ)
Here, SQRT means square root
= SQRT 2AO ÷ C
= SQRT 2 × 40,000 × Rs 10,000 ÷ Rs 2
= SQRT 4,00,000,000
= 20,000 units
(b) No. of procurement to be made during the month (EOQ in order)
= A ÷ EOQ
= 40,000 ÷ 20,000
= 2 times
2058, Q: 7
Following extracted information is given to you:
Estimated annual demand 27,000 units @ Rs 2.50 per unit
Cost to process a purchase order Rs 200
Holding cost Rs 1.20 per unit per year
Safety stock 10% EOQ units
Daily uses 150 units
Lead time 8 days
Required: (a) EOQ units; (b) EQO in order; (c) Total cost at EOQ; (d) Length of inventory cycle
[Answer: (a) EOQ = 3,000 units; (b) EOQ in order = 9 times;
(c) EOQ cost = Rs 3,600; (d) LIC = 20 days]
SOLUTION:
Given and working note:
A = 27,000 units
P = Rs 2.50
O = Rs 200
C = Rs 1.20
Daily uses = 150 units
Days in year = A ÷ Daily uses = 27,000 ÷ 150 = 180 days
(a) EOQ in units
Here, SQRT means square root
= SQRT 2AO ÷ C
= SQRT 2 × 27,000 × Rs 200 ÷ Rs 1.20
= SQRT 9,000,000
= 3,000 units
(b) EOQ in order
= A ÷ EOQ
= 27,000 units ÷ 3,000 units
= 9 times
(c) Total cost at EOQ
Here, SQRT means square root
= SQRT 2AOC
= SQRT 2 × 27,000 × Rs 200 × Rs 1.20
= SQRT 12,960,000
= Rs 3,600
(d) Length of inventory cycle
= Days in a year ÷ EOQ in order
= 180 days ÷ 9 times
= 20 days
Alternatively
= EOQ units ÷ Daily use
= 3,000 units ÷ 150 units
= 20 days
2059, Q: 3
Following extracted information is provided:
Carrying cost per unit Rs 50
Economic order quantity 400 units
Ordering cost per order Rs 2,000
Required: (a) Annual requirement of the materials in units; (b) Minimum average yearly cost;
(c) Optimum number of order per year
[Answer: (a) A = 2,000 units; (b) Total cost = Rs 20,000; (c) Order = 5 times]
SOLUTION:
Given and working note:
C = Rs 50
EOQ = 400 units
O = Rs 2,000
SQRT = square root
(a) Annual requirement of the materials in units 

EOQ 
= SQRT 2AO ÷ C 
400 
= SQRT 2× A × 2,000 ÷ 50 
400 
= SQRT 80A 
(400)^{2} 
= 80A squaring both sides 
160,000 
= 80A 
A 
= 160,000 ÷ 80 

= 2,000 units 


(b) Minimum average yearly cost 

EOQ in cost 
= SQRT 2AOC 

= SQRT 2×2,000 × Rs 2,000 × Rs 50 

= SQRT 40,00,00,000 

= Rs 20,000 


(c) Optimum number of order per year 

EOQ in order 
= A ÷ EOQ units 

= 2,000 units ÷ 400 units 

= 5 times 

2060, Q: 7
AB Trading House has been procuring 80,000 units costing Rs 100 each in 20 installments. The procurement cost is Rs 500 per procurement and the estimated storing cost is 20% inventory value.
Required: (By applying formula where necessary)
(a) Order size of existing and optimum; (b) Total cost of the existing purchasing policy
(c) Total cost of optimum purchasing policy; (d) Saving of optimum purchasing policy is adopted
[Answer: (a) Order size = 4,000 units and 2,000 units; (b) TC existing = Rs 50,000;
(c) TC optimum = Rs 40,000; (d) Saving = Rs 10,000;
SOLUTION:
Given and working note:
Annual procure [A] = 80,000 units
Cost per unit [P] = Rs 100
EOQ in order = 20 order
Procurement cost [O] = Rs 500
Storing cost[C] = Rs 100 @ 20% = Rs 20
Order size [Q] existing
= A ÷ No. of order
= 80,000 units ÷ 20 order
= 4,000 units
Order size [Q] optimum
Here, SQRT means square root
= SQRT 2 × 80,000 × Rs 500 ÷ Rs 20
= SQRT 40,00,000
= 2,000 units
Total cost of the existing purchasing policy
= (AO ÷ Q) + (QC ÷ 2)
= (80,000 × 500 ÷ 4,000) + (4,000 × 20 ÷ 2)
= Rs 10,000 + Rs 40,000
= Rs 50,000
Total cost of the optimum purchasing policy
= (AO ÷ Q) + (QC ÷ 2)
= (80,000 × 500 ÷ 2,000) + (2,000 × 20 ÷ 2)
= 20,000 + 20,000
= Rs 40,000
Saving if optimum purchasing policy is adopted
= Existing policy – Optimum policy
= 50,000 – 40,000
= Rs 10,000
2060 II, Q: 4 or
A Manufacturing Company has been procuring in a lot size of 2,000 (EOQ) units. Material cost per unit is Rs 25. Ordering cost is Rs 200 and the estimated holding cost is 20% of unit cost per year.
Required: (1) (a) Determine annual requirement in units
(b) EOQ units if the ordering cost increases to Rs 250 and cost per unit decreases to Rs 20
[Answer: (a) 50,000 units; (b 2,500 units]
SOLUTION:
Given and working note:
EOQ = 2,000 units
Cost per unit = Rs 25
Ordering cost [O] = Rs 200
Estimated holding cost [C] = Rs 25 @20% = Rs 5
Determine annual requirement in units
Here, SQRT means square root
EOQ in units 
= SQRT 2AO ÷ C 
2,000 
= SQRT 2× A × 200 ÷ 5 
(2,000)^{2} 
= (2 × A × 200) ÷ 5 squaring both sides 
40,00,000 
= 80 A 
A 
= 40,00,000 ÷ 80 

= 50,000 units 
EOQ units if the order costing increases to Rs 250 and cost per unit is decreases to Rs 20
New ordering cost [O] = Rs 250
New cost per unit [P] = Rs 20
New holding cost [C] = Rs 20@20% = Rs 4
EOQ in units
Here, SQRT means square root
= SQRT 2AO ÷ C
= SQRT 2 × 50,000 × Rs 250 ÷ Rs 4
= SQRT 62,50,000
= 2,500 units
2061 I, Q: 5 Or
The following constraints to in procurement have been established for XYZ Ltd:
Annual requirement is 3,00,000 units
Unit purchase price Rs 8
Holding cost is 25% of the purchase price
Economic order quantity is 6,000 units
Required: (a) Ordering cost per order; (b) Total cost at EOQ;
[Answer: (a) Ordering cost = Rs 120; (b) TC = Rs 12,000]
SOLUTION:
Given and working note:
Annual requirement [A] = 300,000 units
Cost per unit = Rs 8
Holding cost = Rs 8@25% = Rs 2
EOQ units = 6,000
Ordering cost per unit [O]
Here, SQRT means square root
EOQ in units 
= SQRT 2AO ÷ C 
6,000 
= SQRT 2×300,000×O ÷ 2 
(6,000)^{2} 
= (2 × 300,000 × O) ÷ 2 squaring both sides 
36,000,000 
= 300,000 × O 
O 
= 36,000,000 ÷ 300,000 

= Rs 120 
Total cost at EOQ [EOQ cost]
Here, SQRT means square root
= SQRT 2AOC
= SQRT 2 × 300,000 × Rs 120 × Rs 2
= SQRT 14,40,00,000
= Rs 12,000
2061 II, Q: 5 Or
Consider the following extracted information of ABC Manufacturing Company:
Re ordering quantity of a part 2,000 units
Holding cost per year Rs 2.5
Cost per unit of part Rs 12.5
Estimated working days in a year 250 days
Procuring cost Rs 250 per order.
Required: (a) Annual demand for a part in units; (b) Average period between the orders
[Answer: A = 20,000 units; Order = 25 days]
*Period = (EOQ units × Days in year) ÷ Annual require
SOLUTION:
Given and working note:
ROQ [EOQ] = 2,000 units
Handling cost per units/year [C] = Rs 2.5
Cost per unit = Rs 12.5
Estimated working days in year = 250 days
Procurement cost [O] per order = Rs 250
Annual demand for a part in units [A]
Here, SQRT means square root
EOQ in units 
= SQRT 2×AO ÷ C 
2,000 
= SQRT 2×A×250 ÷ 2.5 
(2,000)^{2} 
= (2 × A × 250) ÷ 2.5 squaring both sides 
40,00,000 
= 200 A 
A 
= 4,000,000 ÷ 200 

= 20,000 units 
Average period between the orders
= EOQ units × Days in year ÷ Annual require
= 2,000 units × 250 days ÷ 20,000 units
= 25 days
2062, Q: 5
Following extracted information for inventory requirement were given:
Yearly demand for use 40,000 units
Reorder quantity 4,000 units
Procuring cost per procurement Rs 100
Cost per unit of material Rs 2
Required: (a) Holding cost per unit per year; (b) Total cost at order size of 8,000 units after two percent discount
[Answer: HC = Re 0.50; TC = Rs 80,900] *TC = (PV ̶ Discount) + AO÷Q + QC÷2
SOLUTION:
Given and working note:
Yearly demand for use = 40,000 units
Reorder quantity = 4,000 units
Procurement cost [O] = Rs 100
Cost per unit = Rs 2
Holding cost [C]
Here, SQRT means square root
EOQ in units 
= SQRT 2×AO ÷ C 
4,000 
= SQRT 2×40,000×100 ÷ C 
(4,000)^{2} 
= (2 × 40,000 × 100) ÷ C squaring both sides 
16,000,000 
= 800,000 ÷ C 
C 
= 16,000,000 ÷ 8000,000 

= Re 0.50 
Total cost at order size of 8,000 units after 2% discount
Order size [Q] = 8,000 units
Purchase cost = Annual demand × Cost per unit
= 40,000 units × Rs 2
= Rs 80,000
Discount = 80,000@ 2% = Rs 1,600
Now, Total cost
= [Purchase cost – Discount] + Ordering cost + Carrying cost
= [Purchase cost – Discount] + (AO ÷ Q) + (QC ÷ 2)
= (Rs 80,000 – 1,600) + (40,000 × Rs 100 ÷ 8,000) + (80,000 × Re 0.5 ÷ 2)
= Rs 78,400 + Rs 500 + Rs 2,000
= Rs 80,900
2064, Q: 5 Or
Volt Guard Supplier is working for minimizing investment in inventory. The supplier is confident that the annual demand of volt guard will be 10,000 units for the current year. The cost estimated for placing and receiving delivery is Rs 10,000. The estimated storage costs including the opportunity costs of the investment in and store related are Rs 50 per unit per year.
Required: (1) EOQ by using formula and trial and error method
[Answer: EOQ: by formula = 2,000 units; by T&E = 2,000 units]
SOLUTION:
Given and working note:
Annual demand [A] = 10,000 units
Placing and receiving [O] = Rs 10,000
Storage cost [C] = Rs 50 per unit/year
Economic order quantity in units
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 10,000 × Rs 10,000 ÷ Rs 50
= SQRT 40,00,000
= 2,000 units
EOQ by Trial and Error Method
No. of order 
a 
working note 
1 
2 
4 
5 
8 
Order size 
b 
A ÷ a 
10,000 
5,000 
2,500 
2,000 
1,250 
Average quantity 
c 
b ÷ 2 
5,000 
2,500 
1,250 
1,000 
625 
Carrying cost 
d 
c × Rs 50 
250,000 
125,000 
62,500 
50,000 
31,250 
Ordering cost 
e 
a × Rs 10,000 
10,000 
20,000 
40,000 
50,000 
80,000 
Total cost 
f 
d + e 
260,000 
145,000 
102,500 
100,000 
111,250 
Less: Discount 
g 
working note 
Nil 
Nil 
Nil 
Nil 
Nil 
Net cost 
h 
f – g 
260,000 
145,000 
102,500 
100,000 
111,250 
Therefore,
Minimum net cost is Rs 100,000 at 2,000 units in 5^{th} order.
Therefore, EOQ by trial and error method is 2,000 units.
2066, Q: 5 Or
ABC Manufacturing Company buys its annual requirement of 18,000 units in three installments. Each unit cost Re 1 and ordering cost is Rs 25. The inventory carrying cost is estimated at 10% of unit cost.
Required: (1) Order size (Q); (2) Total cost of existing inventory policy without materials cost; (3) Total cost at EOQ
[Answer: (1) Q = 6,000 units (2) TC = Rs 375; (3) TC = Rs 300]
SOLUTION:
Given and working note:
Annual require (A) = 18,000 units
Cost per unit (CPU) = Re 1
Ordering cost (O) = Rs 25
Carrying cost (C) = Re 1 @ 10% = Re 0.10
Order size (Q)
= A ÷ No. of order
= 18,000 units ÷ 3 installments
= 6,000 units
Total cost of the existing purchasing policy
= (AO ÷ Q) + (QC ÷ 2)
= (18,000 × Rs 25 ÷ 6,000) + (6,000 × Re 0.10 ÷ 2)
= Rs 75 + Rs 300
= Rs 375
Total cost at EOQ [EOQ cost]
Economic order quantity
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 18,000 × Rs 25 ÷ Re 0.10
= SQRT 90,000
= 300 units
2067, Q: 5 Or
A Factory buys certain components at Rs 40 per unit. Total annual needs of components are 5,000 units. Carrying cost of inventory is 10% per annum and ordering cost is Rs 100 per order. If the factory orders 5,000 units at a time, the factory will get a 4% discount from the suppliers. The discount policy does not affect the inventory carrying cost.
Required: (a) Economic order quantity; (b) Total cost at EOQ with materials for existing and offer
(c) Advise whether the discount can be accepted?
[Answer: EOQ units = 500 units; Exiting cost = Rs 202,000; Offered = Rs 202,100]
Proposed cost = Rs 202,100; Discount policy cannot be accepted;
SOLUTION:
Given and working note:
Cost per unit (P) = Rs 40
Consumption during the year (A) = 5,000 units
Carrying cost (C) = 40@10 % = Rs 4
Ordering cost (O) = Rs 100
Order size proposed = 5,000 units
(a) Economic order quantity
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 5,000 × Rs 100 ÷ 4
= SQRT 250,000
= 500 units
(b) Total cost with materials for existing purchasing policy
Here, SQRT means square root.
Order size is NOT given
= PA + SQRT 2AOC
= (5,000 × Rs 40) + SQRT 2 × 5,000 × 100 × 4
= Rs 200,000 + SQRT 4,000,000
= Rs 200,000 + Rs 2,000
= Rs 202,000
Total cost with materials for offer
Value of materials = 5,000 units × Rs 40 = Rs 200,000
Discount = 200,000 @ 4% = Rs 8,000
Order size (Q) = 5,000 units
= (AP – Discount) + (A×O ÷ Q) + (Q×C ÷ 2)
= (Rs 200,000 – 8,000) + (5,000 × Rs 100 ÷ 5,000) + (5,000 × Rs 4 ÷ 2)
= Rs 192,000 + Rs 100 + Rs 10,000
= Rs 202,100
(c) Advise whether the discount can be accepted?
Total cost with discount policy is more than existing policy.
Therefore, discount offer cannot be accepted.
2068, Q: 5
The standard consumption of raw materials in a biscuit factory is 2.50 kg of flour for the production of one packet of biscuit. The factory purchases flour on lot basis for which it incurs purchase expenses of Rs 1,250 on each purchase. The total storing cost is Re 0.50 per kg per year. The factory has recently finalized 50,000 packets of biscuit of production plan for the coming year.
Required: EOQ of flour by using trial and error method
[Answer: EOQ = 25,000 kg]
SOLUTION:
Given and working note:
Annual demand [A] = 2.5 kg × 50,000 packets = 125,000 kg
Purchase expenses [O] = Rs 1,250
Storing cost [C] = Re 0.50 per unit/year
Economic order quantity in kg
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 125,000 × Rs 1,250 ÷ Re 0.50
= SQRT 62,50,00,000
= 25,000 kg
EOQ by Trial and Error Method
No. of order 
a 
working note 
1 
2 
4 
5 
8 
Order size 
b 
A ÷ a 
125,000 
62,500 
31,250 
25,000 
15,625.00 
Average quantity 
c 
b ÷ 2 
62,500 
31,250 
15,625 
12,500 
7,812.50 
Carrying cost 
d 
c × Re 0.50 
31,250 
15,625 
7,812.50 
6,250 
3,906.25 
Ordering cost 
e 
a × Rs 1,250 
1,250 
2,500 
5,000.00 
6,250 
10,000.00 
Total cost 
f 
d + e 
32,500 
18,125 
12,812.50 
12,500 
13,906.25 
Less: Discount 
g 
working note 
Nil 
Nil 
Nil 
Nil 
Nil 
Net cost 
h 
f – g 
32,500 
18,125 
12,812.50 
12,500 
13,906.25 
Therefore,
Minimum net cost is Rs 12,500 at 25,000 units in 5^{th} order.
Therefore, EOQ by trial and error method is 25,000 units.
2069, Q: 5
Following extracted information are provided:
Annual requirement of raw materials 50,000 units
Ordering cost per order Rs 500
Opportunity cost Re 1 per unit
Cost of deterioration, insurance and tax Re 1 per unit
Required: (a) Economic order quantity; (b) Cost of ordering 5 times if Rs 2,000 discount avails from supplier
[Answer: (a) 5,000 units; (b) (Rs 12,500 – Rs 2,000) = Rs 10,500]
SOLUTION:
Given and working note:
A = 50,000 units
O = Rs 500
C = (1+1) = Rs 2
(a) Economic order quantity in unit
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 50,000 × Rs 500 ÷ Rs 2
= SQRT 25,000,000
= 5,000 units
(b) Total cost without materials; ordering size 5 times if Rs 2,000 discount avails from supplier
Order size (Q) = 50,000 ÷ 5 times = 10,000 units
= (A×O ÷ Q) + (Q×C ÷ 2)
= (50,000 × Rs 500 ÷ 10,000) + (10,000 × Rs 2 ÷ 2)
= Rs 2,500 + Rs 10,000
= Rs 12,500
Again,
Ordering 5 times if Rs 2,000 discount = Rs 12,500 – Rs 2,000 = Rs 10,500
2070, Q: 5 Or
The annual consumption of raw materials of a factory is 50,000 kg. The cost price per kg is Rs 5. The estimated expense for each purchase is Rs 125. The overall storage cost estimated is 10% of unit inventory cost.
The supplier of the raw materials has made a special offer of 0.2% price off on 10,000 kg lot purchase.
Required: Suggestion for the purchase of raw materials by showing comparative (a) total cost including cost of raw materials for optional purchase; (b) special offer
[Answer:
SOLUTION:
Given and working note:
A = 50,000 kg
P = Rs 5
O = Rs 125
C = Rs 5@10% = Re 0.50
(a) Total cost with materials for existing purchasing policy
Here, SQRT means square root
= PA + SQRT 2AOC
= (50,000 × Rs 5) + SQRT 2 × 50,000 × 125 × 0.50
= Rs 250,000 + SQRT 6,250,000
= Rs 250,000 + Rs 2,500
= Rs 252,500
(b) Total cost with materials for special offer
Value of materials = 50,000 units × Rs 5 = Rs 250,000
Discount = 250,000 @ 0.2% = Rs 500
Order size (Q) = 10,000 units
= (AP – Discount) + (A×O ÷ Q) + (Q×C ÷ 2)
= (Rs 250,000 – 500) + (50,000 × Rs 125 ÷ 10,000) + (10,000 × Re 0.5 ÷ 2)
= Rs 249,500 + Rs 625 + Rs 2,500
= Rs 252,625
(c) Advise whether the discount can be accepted?
Total cost with discount policy is more than existing policy.
Therefore, discount offer cannot be accepted.
2072/Old II, Q: 3 Or
The following extracted information are provided to you:
Per day consumption 20 units
Ordering cost per order Rs 2,000
Carrying cost per unit 20% of inventory value
Interest on loan Rs 3.2 per unit
Cost of materials Rs 20 per unit
Assume 360 days in a year
Required: (a) EOQ; (b) Total cost if the supplier is providing a discount facility of 4%, if purchase in a lot of 3,600 units
[Answer: (a) EOQ = 2,000 units; (b) Total cost = Rs 11,200]
SOLUTION:
A = 360 days × 20 units = 7,200 units
O = Rs 2,000
P = Rs 20
C = Rs 20@20% + Rs 3.2 = 4+3.2 = Rs 7.2
(a) Economic order quantity in unit
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 7,200 × Rs 2,000 ÷ Rs 7.2
= SQRT 4,000,000
= 2,000 units
(b) Total cost excluding materials for special offer
Value of materials (A×P) = 7,200 units × Rs 20 = Rs 144,000
Discount = 144,000 @ 4% = Rs 5,760
Order size (Q) = 3,600 units
= (A×O ÷ Q) + (Q×C ÷ 2) – Discount
= (7,200 × Rs 2,000 ÷ 3,600) + (3,600 × Rs 7.2 ÷ 2) – Rs 5,760
= Rs 4,000 + Rs 12,960 – Rs 5,760
= Rs 11,200
Alternatively,
Total cost excluding materials
Here, SQRT is square root
= SQRT 2AOC
= SQRT 2× 7,200 × Rs 2,000 × Rs 7.2
= SQRT 20,73,00,000
= Rs 14,400
Total cost excluding materials for special offer
Value of materials (A×P) = 7,200 units × Rs 20 = Rs 144,000
Discount = 144,000 @ 4% = Rs 5,760
Order size (Q) = 3,600 units
= (A×O ÷ Q) + (Q×C ÷ 2) – Discount
= (7,200 × Rs 2,000 ÷ 3,600) + (3,600 × Rs 7.2 ÷ 2) – Rs 5,760
= Rs 4,000 + Rs 12,960 – Rs 5,760
= Rs 11,200
Advise whether the discount can be accepted?
Total cost with discount policy is less than existing policy.
Therefore, discount offer can be accepted.
2072/Old I, Q: 3 Or
A Manufacturing Company purchases 2,000 units of particulars item per year at Rs 20 per unit. The ordering cost per order is Rs 50 and the inventory carrying cost is 25% of inventory value.
Find out optimal order quantity and total cost at that quantity.
Should the company accept an offer of a 3% discount at the purchase of 1,000 items at a time?
[Answer: (a) EOQ = 200 units; (b) Total cost = Rs 1,000;
(c) Total cost = Rs 1,400; (d) No; should not accept]
SOLUTION:
A = 2,000 units
P = Rs 20
O = Rs 50
C = Rs 20@25% = Rs 5
(a) Optimal order quantity in unit (EOQ)
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 2,000 × Rs 50 ÷ Rs 5
= SQRT 40,000
= 200 units
(b) Total cost excluding materials
Here, SQRT is square root
= SQRT 2AOC
= SQRT 2× 2,000 × Rs 50 × Rs 5
= SQRT 10,00,000
= Rs 1,000
(c) Total cost excluding materials for special offer at 3% discount
Value of materials (A×P) = 2,000 units × Rs 20 = Rs 40,000
Discount = 40,000 @ 3% = Rs 1,200
Order size (Q) = 1,000 units
= (A×O ÷ Q) + (Q×C ÷ 2) – Discount
= (2,000 × Rs 50 ÷ 1,000) + (1,000 × Rs 5 ÷ 2) – Rs 1,200
= Rs 100 + Rs 2,500 – Rs 1,200
= Rs 1,400
(d) Advise whether the discount can be accepted?
Total cost with discount policy is more than existing policy.
Therefore, discount offer cannot be accepted.
2073/Old, Q: 5 Or
The following extracted particulars of A Manufacturing Firm are provided to you:
Annual requirement of inventory 40,000 units
Purchase price of inventory Rs 20 per unit
Carrying cost 10% of inventory value
Ordering cost per order Rs 400
Required: (a) Economic order quantity (EOQ); (b) Total cost at EOQ;
(c) If the firm purchases its requirement of inventory at a time, the supplier will provide 2% quantity discount. Whether the offer can be accepted or not?
[Answer: (a) EOQ = 4,000 units; (b) Total cost = Rs 8,000;
(c) Total cost = Rs 24,400; (d) No]
SOLUTION:
A = 40,000 units
P = Rs 20
O = Rs 400
C = Rs 20@10% = Rs 2
(a) Optimal order quantity in unit (EOQ)
Here, SQRT is square root
= SQRT 2AO ÷ C
= SQRT 2× 40,000 × Rs 400 ÷ Rs 2
= SQRT 16,000,000
= 4,000 units
(b) Total cost excluding materials
Here, SQRT is square root
= SQRT 2AOC
= SQRT 2× 40,000 × Rs 400 × Rs 2
= SQRT 64,000,000
= Rs 8,000
(c) Total cost excluding materials for special offer at 3% discount
Value of materials (A×P) = 40,000 units × Rs 20 = Rs 800,000
Discount = 800,000 @ 2% = Rs 16,000
Order size (Q) = 40,000 units
= (A×O ÷ Q) + (Q×C ÷ 2) – Discount
= (40,000 × Rs 400 ÷ 40,000) + (40,000 × Rs 2 ÷ 2) – Rs 16,000
= Rs 400 + Rs 40,000 – Rs 16,000
= Rs 24,400
(d) Advise whether the discount can be accepted?
Total cost with discount policy is more than existing policy viz Rs 24,400 > Rs 8,000
Therefore, discount offer cannot be accepted.
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