I have some difficulties with following problem
(I need the solution urgently for tomorrow):
Production levels for Giles Fashion vary greatly according to consumer
acceptance of the latest styles. Therefore, the company's
weekly orders of wool cloth are difficult
to predict in advance. On the basis of 5 years data, the following
probability distribution for the company's weekly demand for wool
has been computed:
Amount of wool (lb) Probability
2500 0.30
3500 0.45
4500 0.20
5500 0.05
>From these data, the raw-materials purchaser computed the
expected number of pounds required. Recently, she noticed
that the company's sales were lower in the last year than in years
before.
Extrapolating, she observed that the company will be lucky
if its weekly demand averages 2,500 this year.
(a) What was the expected weekly demand for wool based
on the distribution from past data?
(b) If each pound of wool generates $5 in revenue and costs $4 to
purchase, ship, and handle, how much would Giles Fashion stand
to gain or lose each week if it orders wool based on the past
expected value and company's demand is only 2,500?
(End of the text of the problem.)
Possible solution (in my opinion):
I.
(a) I fink is obvious: If X means company's weekly demand for wool
(lb), then the expected weekly demand for wool based on the
distribution from past data =E(X) =
0.3*2500+0.45*3500+0.20*4500+0.05*5500=
= 3500. Am I right?
(b)
Actually I am not sure what company's weekly demand for
wool in the past data (table of probability distr.) means.
It is the amount of wool which company bought weekly
or is the amount of wool which company sold (in it's products)
weekly?
The last sentence make difference between
company's orders (it orders wool based...) and company's demand
( and company's demand is only 2,500)
(I think but I am not sure, it's actually company's weekly demand for
wool).
So In my opinion company's weekly demand for wool means:
the amount of wool which company sold (in it's products) weekly?
Am I right?
I am not sure what the last sentence means.
Does it mean that the company orders weekly
3500 lb of wool ( it orders wool based on the past
expected value and the past expected value = 3500 from (a))
and it sells weekly 2500 lb in their products
(and company's demand is only 2,500)?
If so the solution seems to be:
The company should expect to gain weekly: 2500*1$-1000*4$=-1500$
so in fact it should expect to lose weekly 1500$.
--
Am I right?
Maybe I should consider that the company's weekly demand
is 2500 lb but it orders are:
Amount of wool (lb) Probability
2500 0.30
3500 0.45
4500 0.20
5500 0.05
(Loss | Orders=2500 ) 0$ -1500$ ...
probability 0.30 0.45
E(Loss | Orders=2500 ) = 0*0.3+(-1500)*0.45+ ...
Please somebody correct me if I am wrong.
Jan
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
