United Aluminum Company: Sensitivity analysis
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United Aluminum Company of Cincinnati produces three grades of aluminum at two mills. Each mill has a different production capacity for each grade as follows:
Mill
aluminum
grade------------------------ 1 2
----------------------------------------------------------------------------
high 6 2
medium 2 2
low 4 10
The company has contacted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium grade aluminum and 5 tons of low grade aluminum. It costs United $6000 per day to operate mill 1 and $7000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost.
a) identify and explain the shadow prices for each of the aluminum grade contract requirements.
b) identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.
c) would the solution values change if the contract requirements for high grade aluminum were increased from 12 tons to 20 tons? if yes what would the new solution values be?
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