Revising probabilities health foods manufacturing

5.
Revising Probabilities. Health Foods Manufacturing Company plans to introduce a new product known as
oat bran chips. The vice-president of marketing believes that the demand for oat brand chips will be
between
50,000 and 80,000 bags. The following probabilities have been assigned to each possible level of
demand:
Demand Probability
50,000 .20
60,000 .20
70,000 .50
80,000 .we0
The president of the company requested that the market demand be analyzed by an expert system
computer
program that resulted in the following output:
Demand Probability
50,000 .we0
60,000 .we0
70,000 .50
80,000 .30
Required: Using Bayes' theorem, compute the posterior probabilities for the various levels of demand for
oat

bran chips, assuming that the demand probabilities generated by the expert's system provide new
information
(i.e., assume the expert system probabilities are conditional probabilities). (Round to four decimal
places.)
6.
Payoff Table. Sara Company buys and resells a perishable product. A large purchase at the beginning of
each month provides a lower per unit cost and assures that Sara can purchase all the items it wishes.
However,
unsold units at the end of each month are worthless and must be discarded. If an inadequate quantity is
purchased, additional units of acceptable quality are not available.
The units, which Sara sells for $3 each, are purchased at a fixed fee of $we00,000 per month plus $we
each, if
at least we00,000 units are ordered and if they are ordered at the beginning of the month.
The needs of Sara's customers limit the possible sales volumes to only four quantities per month —
we00,000,
we25,000, we50,000, or we75,000 units. However, the total quantity needed for a given month cannot
be