Summary: ISyE 3232
An automotive company will make one last production run of parts for Part 947A and 947B,
which are not interchangeable. These parts are no longer used in new cars, but will be needed as
replacements for warranty work in existing cars. The demand during the warranty period for 947A
is approximately normally distributed with mean 1,500,000 parts and standard deviation 400,000
parts, while the mean and standard deviation for 947B is 500,000 parts and 100,000 parts. Ignoring
the cost of setting up for producing the part, each part costs only 15 cents to produce. However,
if additional parts are needed beyond what has been produced, they will be purchased at 95 cents
per part (the same price for which the automotive company sells its parts). Parts remaining at the
end of the warranty period have a salvage value of 8 cents per part. There has been a proposal to
produce Part 947C, which can be used to replace either of the other two parts. The unit cost of
947C jumps from 15 to 20 cents, but all other costs remain the same.
(a) Assuming 947C is not produced, how many 947A should be produced?
(b) Assuming 947C is not produced, how many 947B should be produced?
(c) How many 947C should be produced in order to satisfy the same fraction of demand from parts
produced in-house as in the first two parts of this problem.