Question

A car dealer believes that demand for 2018 model will be normally distributed with a mean of 200 and standard deviation of 30. His cost of receiving a car is 25,000 Euros and he sells the same for 40,000 Euros. Half of all leftover cars can be sold for 30,000 Euros. He is considering ordering 200, 220, 240, 260, 280, or 300 cars. How many should he order?

Answer 1

Answer:

Given,

Mean = 200

Standard deviation = 30

Let us consider .

If a car dealer wants to fulfill 99.9% of the service level.

In order to achieve this service level, the car driver needs to maintain inventory of

i.e.,

given as follows

consider,

mean + 3*sigma

substitute values

= 200 + 3*30

= 290

So it is clear that the 290 units will achieve the 99.9 % of the service level.

It is given that half unsold units can still be sold at $ 30000

So that there is no loss.

So finally, If he orders 300, then there is a possible loss on unsold given 5 items.

So we conclude that, it is advisable to order 280 units.