Exercise 6.3 - Chapter 6 - Application of Differentiation - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 6.3

Text Book Back Questions and Answers

Question 1.
The following table gives the annual demand and unit price of 3 items

Ordering cost is  5 per order and holding cost is 10% of unit price. Determine the following:
(i) EOQ in units
(ii) Minimum average cost
(iii) EOQ in rupees
(iv) EOQ in years of supply
(v) Number of orders per year
Solution:
Item A:
Demand rate, R = 800
Ordering cost, C₃ = ₹ 5
Carrying cost C₁ = 10% of unit price

(i) EOQ in units

(ii) Minimum Average Cost

=4

(iii) EOQ in rupees = EOQ × Unit price
= 2000 × 0.02

=40

Item B:
Demand rate, R = 400
Ordering cost, C₃ =  5
Carrying cost C₁ = 10% of 1.00

(i) EOQ in units

= 20 × 10
= 200 units

(ii) Minimum Average Cost

=20

(iii) EOQ in rupees = EOQ × unit price
= 200 × 1
= 200

Item C:
Annual Demand, R = 800
Ordering cost, C₃ =  5
Carrying cost, C₁ = 10% of unit price

(i) EOQ in units

= 100 × 26.2678
= 100 × 26.27
= 2627

(ii) Minimum Average Cost 

=52.54

(iii) EOQ in rupees = 2627 × 0.20 = 25.40 [∵ Unit price = 0.20]

Question 2.
A dealer has to supply his customer with 400 units of a product per week. The dealer gets the product from the manufacturer at a cost of ₹ 50 per unit. The cost of ordering from the manufacturers in ₹ 75 per order. The cost of holding inventory is 7.5 % per year of the product cost. Find
(i) EOQ
(ii) Total optimum cost.
Solution:
Demand = 400 units per week
Annual demand = 400 × 52 per year
Ordering cost per order C₃ = 175
Inventory cost C₁ = 7.5% per year of the cost
= 7.5% of 50 per year

(i) EOQ in units

EOQ = 912 units

(ii) Total optimum cost = Purchasing cost + Minimum annual cost

= 20000 + 65.7793
= 20,065.78 per week