A GMC dealer believes that demand for 2005 Envoys will be normally distributed with a mean of 200 and standard deviation of 30. His cost of receiving an Envoy is $25,000, and he sells an Envoy for $40,000. Half of all the Envoys not sold at full price can be sold for $30,000. He is considering ordering 200, 220, 240, 260, 280, or 300 Envoys. How many should he order?

Let's ask that the supplier needs to reach 99.9% of the standard of operation. To reach this quality of operation, she has to preserve an inventory of

Now,

⇒ [tex]Mean + 3\times sigma[/tex]

On putting the values, we get

⇒ [tex]200+3\times 30[/tex]

⇒ [tex]200+90[/tex]

⇒ [tex]290 \ units[/tex]

290 units would then accomplish a level of service of 99.9%.

Half unpurchased units can indeed be purchased at $30000 i.e. no failure. If he requests 300, there will be losses on 5 products that are unsold.

Hence, ordering 280 units seems to be preferable

MrRoyal MrRoyal · Answer 2 · 2021-11-16T21:56:14+01:00

The number of orders follows the 99% empirical rule

He should order 280 2005 Envoys.

The given parameters are:

[tex]\mathbf{\bar x = 200}[/tex]

[tex]\mathbf{\sigma = 30}[/tex]

Using the 99% empirical rule the number of orders (n) is:

[tex]\mathbf{n = \bar x + 3 \times \sigma}[/tex]

So, we have:

[tex]\mathbf{n = 200 + 3 \times 30}[/tex]

Multiply

[tex]\mathbf{n = 200 + 90}[/tex]

Add

[tex]\mathbf{n = 290}[/tex]

From the list of given options, 280 is the closest order that is less than 290.

Hence, he should order 280 2005 Envoys.