Question

A dealer supplies you the following information with regard to a product dealt in by him.

Annual demand = 5000 units;

Buying Cost = . 250.00 per order

Inventory carrying cost = 30% per year

Price = . 100 per unit

The dealer is considering the possibility of allowing Home back orders to occur for the
product. He has estimated that the annual cost of back ordering (allowing shortages) the
product will be Rs. 10.00 per unit.

(i) What should be the optimum number of units of the product he should buy in one lot?

(ii) What quantity of the product should he allow to be back-ordered?

(iii) How much additional cost will he have to incur on Inventory if he does
not permit back-ordering?​

Answer 1

Answer:

Let the initial velocity of the body be u m/s; and the constsnt acceleration be a m/s². Then displacemet (distance covered) of the body after t second is given by

s = u t + ½ a t² ———————————-(1)

The body covers 20 m in 2s and 80 m in 4 s.

20 = u×2 + ½ a 2²; => 20 = 2 u + 2 a

u + a = 10 —————————————(2)

80 = u×4 + ½ a 4²; => 80 = 4 u + 8 a; this gives,

u + 2 a = 20 ——————————————(3)

Solving (2) and (3) for u and a we get

u = 0 m/s and a = 10 m/s² ————————(4)

To obtain the distance covered in the next 4s we need to find the velocity at the beginning of this interval using,

v = u + a t => v = 0