6-30 After analyzing the costs of various options for obtaining brackets, Ross White (see Problems 6-27 through 6-29) recognizes that although he knows that the lead time is 2 days and the demand per day averages 10 units, the demand during the lead time often varies. Ross has kept very careful records and has determined that lead time demand is normally distributed with a standard deviation of 1.5 units.(a) What Z value would be appropriate for a 98% service level?(b) What safety stock should Ross maintain if he wants a 98% service level?(c) What is the adjusted ROP for the brackets?(d) What is the annual holding cost for the safety stock if the annual holding cost per unit is $1.50?I'm stuck on c and d nave to de ! II ine carryıng cost was 10% Of ine cost,pracket iI Ross wouia purcnase ine orackets in lotswhat would the optimal order quantity be?: 6-26 In Problem 6-20, you helped Lila Battle determine theoptimal order quantity for number 6 screws. She hadestimated that the ordering cost was $10 per order. Atthis time, though, she believes that this estimate wastoo low. Although she does not know the exact order-ing cost, she believes that it could be as high as $40 perorder. How would the optimal order quantity change ifthe ordering cost were $20, $30, and $40?: 6-27 Ross White's machine shop uses 2,500 brackets dur-ing the course of a year, and this usage is relativelyconstant throughout the year. These brackets are pur-chased from a supplier 100 miles away for $15 each,and the lead time is 2 days. The holding cost perbracket per year is $1.50 (or 10% of the unit cost),and the ordering cost per order is $18.75. There are250 working days per year.of 1,000. Lead times, however, would increase to 3days for this larger quantity.(a) What is the total annual inventory cost plus pur-chase cost if Ross buys the brackets in lots of1,000 at $14.50 each?(b) If Ross does buy in lots of 1,000 brackets, whatis the new ROP?(c) Given the options of purchasing the brackets at$15 each, producing them in-house at $14.80,and taking advantage of the discount, what isyour recommendation to Ross White?:6-30 After analyzing the costs of various options for ob-taining brackets, Ross White (see Problems 6-27through 6-29) recognizes that although he knowsthat the lead time is 2 days and the demand per dayaverages 10 units, the demand during the lead timeoften varies. Ross has kept very careful records andhas determined that lead time demand is normally(a) What is the EOQ?(b) Given the EOQ, what is the average inventory?What is the annual inventory holding cost?(c) In minimizing cost, how many orders would beplaced each year? What would be the annualordering cost?(d) Given the EOQ, what is the total annual inven-tory cost (including purchase cost)?(e) What is the time between orders?(f) What is the ROP?distributed with a standard deviation of 1.5 units.(a) What Z value would be appropriate for a 98%service level?(b) What safety stock should Ross maintain if hewants a 98% service level?(c) What is the adjusted ROP for the brackets?(d) What is the annual holding cost for the safetystock if the annual holding cost per unit is $1.50?: 6-28 Ross White (see Problem 6-27) wants to reconsiderhis decision of buying the brackets and is consider-ing making the brackets in-house. He has determinedthat setup cost would be $25 in machinist time andlost production time and that 50 brackets could beproduced in a day once the machine has been set up.Ross estimates that the cost (including labor timeand materials) of producing one bracket would be$14.80. The holding cost would be 10% of this cost.:6-31 Annual demand for the Dobbs model airplane kit is80,000 units. Albert Dobbs, president of Dobbs' Ter-rific Toys, controls one of the largest toy companiesin Nevada. He estimates that the ordering cost is $40per order. The carrying cost is $7 per unit per year. Itis 25 days from the time that Albert places an orderfor the model airplane kits until they are received athis warehouse. During this time, the daily demand isestimated to be 450 units.(a) What is the daily demand rate?(b) What is the optimal production quantity?(c) How long will it take to produce the optimalquantity? How much inventory is sold duringthis time?(a) Compute the EOQ, ROP, and optimal number oforders per year.(b) Albert now believes that the carrying cost maybe as high as $14 per unit per year. Furthermore,he estimates that the lead time may be 35 daysinstead of 25 days. Redo part (a), using these re-vised estimates.(d) If Ross uses the optimal production quantity,what would be the maximum inventory level?What would be the average inventory level?What is the annual holding cost?(e) How many production runs would there be eachyear? What would be the annual setup cost?(f) Given the optimal production run size, what isthe total annual inventory cost?(g) If the lead time is one-half day, what is the ROP?:6-32 Morgan Arthur has spent the past few weeks deter-mining inventory costs for Armstrong, a toy manu-facturer located near Cincinnati, Ohio. She knowsthat annual demand will be 30,000 units per year andthat the carrying cost will be $1.50 per unit per year.The ordering cost, on the other hand, can vary from$45 per order to $50 per order. During the past 450working days, Morgan has observed the followingfrequency distribution for the ordering cost::6-29 Upon hearing that Ross White (see Problems 6-27and 6-28) is considering producing the brackets in-house, the vendor has notified Ross that the purchase

Given: Lead time = 2 days The standard deviation of demand = 1.5 units. Average demand per day =…

Answered: 6-30 After analyzing the costs of…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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6-30 After analyzing the costs of various options for obtaining brackets, Ross White (see Problems 6-27 through 6-29) recognizes that although he knows that the lead time is 2 days and the demand per day averages 10 units, the demand during the lead time often varies. Ross has kept very careful records and has determined that lead time demand is normally distributed with a standard deviation of 1.5 units.

(a) What Z value would be appropriate for a 98% service level?

(b) What safety stock should Ross maintain if he wants a 98% service level?

(c) What is the adjusted ROP for the brackets?

(d) What is the annual holding cost for the safety stock if the annual holding cost per unit is $1.50?

I'm stuck on c and d

nave to de ! II ine carryıng cost was 10% Of ine cost,
pracket iI Ross wouia purcnase ine orackets in lots
what would the optimal order quantity be?
: 6-26 In Problem 6-20, you helped Lila Battle determine the
optimal order quantity for number 6 screws. She had
estimated that the ordering cost was $10 per order. At
this time, though, she believes that this estimate was
too low. Although she does not know the exact order-
ing cost, she believes that it could be as high as $40 per
order. How would the optimal order quantity change if
the ordering cost were $20, $30, and $40?
: 6-27 Ross White's machine shop uses 2,500 brackets dur-
ing the course of a year, and this usage is relatively
constant throughout the year. These brackets are pur-
chased from a supplier 100 miles away for $15 each,
and the lead time is 2 days. The holding cost per
bracket per year is $1.50 (or 10% of the unit cost),
and the ordering cost per order is $18.75. There are
250 working days per year.
of 1,000. Lead times, however, would increase to 3
days for this larger quantity.
(a) What is the total annual inventory cost plus pur-
chase cost if Ross buys the brackets in lots of
1,000 at $14.50 each?
(b) If Ross does buy in lots of 1,000 brackets, what
is the new ROP?
(c) Given the options of purchasing the brackets at
$15 each, producing them in-house at $14.80,
and taking advantage of the discount, what is
your recommendation to Ross White?
:6-30 After analyzing the costs of various options for ob-
taining brackets, Ross White (see Problems 6-27
through 6-29) recognizes that although he knows
that the lead time is 2 days and the demand per day
averages 10 units, the demand during the lead time
often varies. Ross has kept very careful records and
has determined that lead time demand is normally
(a) What is the EOQ?
(b) Given the EOQ, what is the average inventory?
What is the annual inventory holding cost?
(c) In minimizing cost, how many orders would be
placed each year? What would be the annual
ordering cost?
(d) Given the EOQ, what is the total annual inven-
tory cost (including purchase cost)?
(e) What is the time between orders?
(f) What is the ROP?
distributed with a standard deviation of 1.5 units.
(a) What Z value would be appropriate for a 98%
service level?
(b) What safety stock should Ross maintain if he
wants a 98% service level?
(c) What is the adjusted ROP for the brackets?
(d) What is the annual holding cost for the safety
stock if the annual holding cost per unit is $1.50?
: 6-28 Ross White (see Problem 6-27) wants to reconsider
his decision of buying the brackets and is consider-
ing making the brackets in-house. He has determined
that setup cost would be $25 in machinist time and
lost production time and that 50 brackets could be
produced in a day once the machine has been set up.
Ross estimates that the cost (including labor time
and materials) of producing one bracket would be
$14.80. The holding cost would be 10% of this cost.
:6-31 Annual demand for the Dobbs model airplane kit is
80,000 units. Albert Dobbs, president of Dobbs' Ter-
rific Toys, controls one of the largest toy companies
in Nevada. He estimates that the ordering cost is $40
per order. The carrying cost is $7 per unit per year. It
is 25 days from the time that Albert places an order
for the model airplane kits until they are received at
his warehouse. During this time, the daily demand is
estimated to be 450 units.
(a) What is the daily demand rate?
(b) What is the optimal production quantity?
(c) How long will it take to produce the optimal
quantity? How much inventory is sold during
this time?
(a) Compute the EOQ, ROP, and optimal number of
orders per year.
(b) Albert now believes that the carrying cost may
be as high as $14 per unit per year. Furthermore,
he estimates that the lead time may be 35 days
instead of 25 days. Redo part (a), using these re-
vised estimates.
(d) If Ross uses the optimal production quantity,
what would be the maximum inventory level?
What would be the average inventory level?
What is the annual holding cost?
(e) How many production runs would there be each
year? What would be the annual setup cost?
(f) Given the optimal production run size, what is
the total annual inventory cost?
(g) If the lead time is one-half day, what is the ROP?
:6-32 Morgan Arthur has spent the past few weeks deter-
mining inventory costs for Armstrong, a toy manu-
facturer located near Cincinnati, Ohio. She knows
that annual demand will be 30,000 units per year and
that the carrying cost will be $1.50 per unit per year.
The ordering cost, on the other hand, can vary from
$45 per order to $50 per order. During the past 450
working days, Morgan has observed the following
frequency distribution for the ordering cost:
:6-29 Upon hearing that Ross White (see Problems 6-27
and 6-28) is considering producing the brackets in-
house, the vendor has notified Ross that the purchase

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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