Harry’s is a chain of 47 self service gas stations served by a small refinery and mixing plant. Each day’s
product requirements are met by blending feedstocks on hand at midnight. The volumes vary daily,
depending on the previous day’s refinery output and on bulk receipts.
The entire operation is run by the owner, Harry Paul. Although dozens of chemicals and byproducts are
generated by the refinery, Harry’s major concern is the retail distribution of gasoline products.
On a particular Tuesday there are significant volumes of leaded and unleaded regular gasolines at the
stations. Only the two hybrid petroleum products – gasohol and petrolmeth – will be shipped that day. Both
products are blended from 90-octane unleaded gasoline. Ethyl alcohol, the only additive to gasohol, cannot
exceed 10% of the final product’s volume. Petrolmeth may contain both ethyl and methyl alcohols, but these
combined ingredients must not exceed 30% of the final product’s volume. The octane ratings are 120 for
ethyl alcohol and 110 for methyl alcohol. Final product octane ratings must equal the average octane ratings
for the ingredients by volume. Gasohol must have an octane rating of at least 91, and petrolmeth must have
a rating of at least 93.
There are 20,000 gallons of gasoline presently available for blending, at a cost of $1.00 per gallon. Up to
5000 gallons of methyl alcohol can be acquired for $0.50 per gallon; 3000 gallons of ethyl alcohol are
available at $1.50 per gallon. The demands are at least 10,000 gallons for gasohol and 5000 gallons for
Until now Harry has determined product blends by trial and error. A new staff analyst says she can save a
considerable amount of money by using LP to establish a minimum cost blending formulation. Harry is a bit
skeptical, but he offers her the challenge to do better than his method.
1. Define an appropriate set of decision variables
2. Formulate a symbolic model for this problem, and solve it.
3. Explain how Harry maybe able to use the optimal solution to support blending decisions.
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