Homework_7_2023
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School
Liberty University *
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Course
361
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
2
Uploaded by BrigadierWillpower11048
Operations Management (Fall 2023)
Homework 7
1. Suppose that the rate of customer demand for candy bars at Grocery City is constant at a rate
of 400 candy bars per week. Each time that Grocery City places an order for more candy bars it
must pay processing fees of
$
25 regardless of the size of the order. Holding costs for candy bars are
$
0.02 per candy bar per week. Finally, leadtime for the delivery of candy bars is 0 days. Assume
that there are 52 weeks in a year.
a.
Suppose that Grocery City places an order for 600 candy bars each time that its inventory
of candy bars reaches 50. Draw a graph showing the number of candy bars that Grocery City has
on-hand in inventory at each point in time up until the time when it places its fourth order. Label
the points in time at which Grocery City places a new order. What will be Grocery City’s average
inventory holding costs per unit time? What will be Grocery City’s average fixed ordering costs
per unit time? Assume that Grocery City starts out with 650 candy bars on day 0.
b.
Assuming that Grocery City would like to minimize the sum of its average purchasing, fixed
ordering and holding costs per unit time, what is the optimal number of candy bars for Grocery
City to purchase each time that it places an order and what should be its reorder point?
c. Suppose now that it takes 2 weeks for each order of candy bars to be delivered. When the
quantity of candy bars reaches what level should Grocery City place an order for more candy bars?
Assume that Grocery City orders according to the optimal order quantity from part b above.
2.
Zara is determining how many coats to order for this upcoming winter selling season.
Zara
forecasts the demand distribution for coats this upcoming winter to be the following.
Demand
(number of coats)
Probability
100
0.1
150
0.1
200
0.2
250
0.3
300
0.2
350
0.1
Each coat costs Zara
$
100 to purchase wholesale and sells for
$
200 retail. At the end of the winter
selling season, Zara may sell as many coats as it desires at a salvage value of
$
50 per coat.
a.
What is the optimal number of coats for Zara to purchase in order to maximize its average
profit?
1
b. Suppose that Zara has purchased 200 coats, what is the marginal value from a 201st coat? Is it
profitable for Zara to purchase its 201st coat? Justify your answer.
3. A pastry shop is considering how much hot chocolate to prepare each morning. Hot chocolate
costs
$
0.10 per oz to make and sells for
$
0.90 per oz.
Customers can buy hot chocolate in any
number of ounces that they wish. Any hot chocolate not sold by the end of the day is discarded.
The daily demand for hot chocolate is normally distributed with a mean of 1,000 oz and a standard
deviation of 50 oz. How much hot chocolate should the pastry shop make each morning? You may
use a z-table for this question.
2
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