Q. 9OQ Sally鈥檚 Silk Screening produce... [FREE SOLUTION]

91影视

Operations And Supply Chain Management

F. Robert Jacobs

Business Studies

14th Edition 路 800 pages

ISBN: 9780078024023

Chapter 4: Q. 9OQ (page 545)

Sally鈥檚 Silk Screening produces specialty T-shirts that are primarily sold at special events. She is trying to decide how many to produce for an upcoming event. During the event, Sally can sell T-shirts for $20 apiece. However, when the event ends, any unsold T-shirts are sold for $4 apiece. It costs Sally $8 to make a specialty T-shirt. Sally鈥檚 estimate of demand is the following:
Demand
Probability
300
.05
400
.10
500
.40
600
.30
700
.10
800
.05
a. What is the service rate (or optimal fractile)?

Short Answer

Expert verified

The profit function and the optimal fractile formula The conventional newsvendor profit function is where is a random variable with a probability distribution indicating demand, each unit is sold and purchased for a price, is the number of units supplied, and is the expectation operator.

Step by step solution

Step 1:Calculation of Service rate (or Optimalfractile)

Given,

The selling price of a T shirt is $20 each

Cost price for making a specialty T shirt is $ 4

Unsold T shirts are sold for $ 4 each

$C o s t o f u n d e r s t o c k i n g = $ 20 - $ 8 = $ 12 C o s t o f o v e r s t o c k i n g = $ 8 - $ 4 = $ 4$

$Service rate= \frac{Cost of under stocking}{Cost of understocking + Cost of overstocking} = \frac{12}{12 + 4} = 0.75$

So, the service rate or optimal fractile is 0.75

Calculation of number of T-shirts that should be produced for an upcoming event

Demand	Probability	Cumulative Probability
300	0.05	0.05 =0.05
400	0.10	0.05+.010 = 0.15

500	0.40	0.05+.010+0.40 = 0.55
600	0.30	0.05+.010+0.40+0.30 = 0.85
700	0.10	0.05+.010+0.40+0.30+0.10 =0.95
800	0.05	0.05+.010+0.40+0.30+0.10+0.05 = 1