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adell [148]
3 years ago
11

Lieutenant Commander Data is planning to make his monthly (every 30 days) trek to Gamma Hydra City to pick up a supply of isolin

ear chips. The trip will take Data about three days. Before he leaves, he calls in the order to the GHC Supply Store. He uses chips at an average rate of seven per day (seven days per week) with a standard deviation of demand of two per day. He needs a 98 percent service probability.
Required:
If he currently has 35 chips in inventory, how many should he order? What is the most he will ever have to order?
Business
1 answer:
nadezda [96]3 years ago
8 0

Answer:

219.57 units

Explanation:

Given :

Daily demand, d = 7 per day

Standard deviation, = 2 per day

Service probability = 98%

Total number of days per week = 7

Lead time , L = 3 days

On hand inventory, I = 35

Now calculating the optimal order quantity by using the given formula,

$q=d(T+L)+ z \ \sigma_{r+L}-I$   .............(i)

First, we will find out the value of  $\sigma_{r+L}$ and z.

Therefore,

$\sigma_{r+L}=\sqrt{(30+3)(2)^2}$

        $=\sqrt{132}$

       = 11.48

Now the value of z can be found out from the z-table,

Z value for 98% service level = 2.054

Now putting the value of $\sigma_{r+L}$ and z in equation (i), we get,

$q=d(T+L)+ z \ \sigma_{r+L}-I$  

   = (7)(30+3)+(2.054)(11.48) - 35

   = 231 + 23.57 - 35

   = 219.57 units

So the optimal number of the units required to be order = 219.57 units

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Year             Cash Flow (A)            Cash Flow (B)

0                      -37,500                      -37,500

1                         17,300                         5,700

2                        16,200                       12,900

3                        13,800                       16,300

4                         7,600                       27,500

1) Using an excel spreadsheet and the IRR function:

IRR project A = 20%

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2) Using the IRR decision rule, Bruin should choose project A.

3) In this case, since the length of the projects is only 4 years, then there should be no problem with the IRR decision rule, but for projects with longer time lengths, the discounts rates might vary and the best option is to use the modified internal rate of return (MIRR). But in this case the NPV of project B is higher, then Bruin should probably project B because it has a higher NPV. The NPV is always more important then the IRR.

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1      $11,600

2     $3,300

3    -$2,500

4   -$19,900

then we calculate the IRR = 16%

Bruin should be indifferent between the two projects at a 16% discount rate. That means that at discount rates above 16%, you should choose project A, but at discount rates below 16%, you should choose project B

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