Decision Analysis

Decision Analysis

Order Description

Imperial College EXECUTIVE EDUCATION
London Data, Models and Decisions
Wolfram Wiesemann
BUSlNESS SCHOOL
Group Assignment
(1) During their spare time in college, Anders and Michael have developed software to regulate
traffic on internet sites. Their product is very original, and they have applied for a patent. They
estimate that there is an 80% chance of their patent being approved.
Last week, Anders and Michael have presented their ideas to Singular Inc., the dominant
player in this market, after Singular had signed a confidentiality agreement with Anders and
Michael. Yesterday, Singular announced a new software product that looks suspiciously similar
to the software that Anders and Michael have developed. Anders suggested to sue Singular
immediately, but Michael felt they should wait until they receive notification of their patent
(which is still pending). Michael reasoned that their case will be much stronger if they had a
patent on the product.
Suppose that Anders and Michael have a 90% chance of winning a lawsuit against Singular
if their patent is approved, and they have a 60% chance of winning a lawsuit while their patent
is still pending. However, if their patent is not approved, then the chance of winning a lawsuit
drops to 40%. In any case, Anders and Michael expect to win $1,000,000 if the lawsuit is
successful. However, they estimate that suing Singular Inc. would cost $100,000, no matter
whether the patent is still pending, approved or rejected.
(a) Using a decision tree, decide what Anders and Michael should do to maximise the
expected profits!
(b) Singular informally makes a “now-or-never” offer to buy Anders’ and Michael’s software
for $500,000. Should Anders and Michael agree to this offer?
(2) The Primo Insurance Company is introducing two new product lines: special risk insurance and
mortgages. The expected profit is $5/unit on special risk insurance and $2/unit on mortgages.
Management wishes to establish sales quotas for the new product lines to maximise the total
expected profit. The work requirements are as follows:
(a) Formulate a linear program for this problem!
f tailgatestg‘;int. T ‘7
v – v Work-hours
Y Department” ‘SpeCi‘éli’riskl “ .1 Mortgage “available
Underwriting 3 2 2,400
Administration 0 1 800
Claims 2 0 1,200
(b) Try to find sales quotas for the new product lines that satisfy the available work-hour
limits and maximise the total expected profits. You do not have to find the optimal
quotas, but you should justify your choice of quotas!

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