Chris sandvig irrigation

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Solved Problems Virtual Office Hours help is available at www.myomlab.com

Solved Problem 12.1

David Alexander has compiled the following table of six items in inventory at Angelo Products, along with the unit cost and the annual demand in units:

Use ABC analysis to determine which item(s) should be carefully controlled using a quantitative inventory technique and which item(s) should not be closely controlled.

Solution

The item that needs strict control is 33CP, so it is an A item. Items that do not need to be strictly controlled are 3CPO, R2D2, and RMS; these are C items. The B items will be XX1 and B66.

70% of

Total cost = $100, 516.56

total cost = $70, 347.92

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Solved Problem 12.2

The Warren W. Fisher Computer Corporation purchases 8,000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per order.

What are (a) the optimal order quantity, (b) the expected number of orders placed each year, and (c) the expected time between orders? Assume that Fisher operates on a 200-day working year.

Solution

a.

b.

c.

With 20 orders placed each year, an order for 400 transistors is placed every 10 working days.

PRINTED BY: stacymarlow@yahoo.com. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

= = = 400 unitsQ∗ 2DS H

− −−√ 2(8,000) (30)3 − −−−−−−−√

N = = = 20 ordersD Q∗

8,000 400

Time between orders = T = = = 10 working dNumber of working days N

200 20

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Solved Problem 12.3

Annual demand for notebook binders at Meyer’s Stationery Shop is 10,000 units. Brad Meyer operates his business 300 days per year and finds that deliveries from his supplier generally take 5 working days. Calculate the reorder point for the notebook binders.

Solution

Thus, Brad should reorder when his stock reaches 167 units.

Solved Problem 12.4

Leonard Presby, Inc., has an annual demand rate of 1,000 units but can produce at an average production rate of 2,000 units. Setup cost is $10; carrying cost is $1. What is the optimal number of units to be produced each time?

Solution

L

d

ROP

=

=

=

5 days

= 33.3 units per day10,000300 d × L = (33.3 units per day)(5 days) = 166.7 units

= =Q∗p 2DS H(1− )Annual demand rate

Annual production rate

− −−−−−−−−−−−−−√ 2(1,000) (10)1[1−(1,000/2,000)] − −−−−−−−−−−√

= = = 200 units20,000 1/2

− −−−√ 40, 000− −−−−−√

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Solved Problem 12.5

Whole Nature Foods sells a gluten-free product for which the annual demand is 5,000 boxes. At the moment, it is paying $6.40 for each box; carrying cost is 25% of the unit cost; ordering costs are $25. A new supplier has offered to sell the same item for $6.00 if Whole Nature Foods buys at least 3,000 boxes per order. Should the firm stick with the old supplier, or take advantage of the new quantity discount?

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Solution

Under the present price of $6.40 per box:

Economic order quantity, using Equation (12-10) :

where

Note: Order and carrying costs are rounded.

Under the quantity discount price of $6.00 per box:

We compute which is below the required order level of 3,000 boxes. So Q* is adjusted to 3,000.

Q∗

Q∗

=

=

=

2DS IP

− −−√ 2(5,000) (25) (0.25) (6.40)

− −−−−−−−√ 395.3, or 395 boxes

D

S

P

I

H

= = = = =

period demand ordering cost price per box holding cost as percent holding cost = IP

Total cost = Order cost + Holding cost + Purchase cost

= + H + PDDS Q

Q

2

= + + (6.40) (5, 000)(5,000) (25)395 (395) (0.25) (6.40)

2

= 316 + 316 + 32, 000 = $ 32, 632

= 408.25,Q∗

= + H + PDDS Q

Q