3.
An oil refinery has two sources of crude oil: a light crude that costs
$35/barrel and a heavy crude that costs $30/barrel. The refinery produces
gasoline, heating oil, and jet fuel from crude in the amounts per barrel
indicated in the following table:
Gasoline Heating oil Jet fuel
Light crude 0.3 0.2 0.3
Heavy crude 0.3 0.4 0.2
The refinery has contracted to supply 900,000 barrels of gasoline,
800,000 barrels of heating oil, and 500,000 barrels of jet fuel.
The refinery wishes to find the amounts of light and heavy crude to
purchase so as to be able to meet its obligations at minimum cost.
Formulate this problem as a linear program.
8.
Convert the following problem to a linear program in standard form:
Minimize |x|+|y|+|z| subject to x+y<=1 and 2x+z=3
15.
Let S be a convex set in E^n and S* a convex set in E^m. Suppose T is
an m*n matrix that establishes a one-to-one correspondence between S and
S*, i.e., for every s\in S there is s*\in S* such that Ts=s*, and for
every s*\in S* there is a single s\in S such that Ts=s*. Show that there
is a one-to-one correspondence between extreme points of S and S*.
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※ 編輯: enorm 來自: 140.112.48.60 (02/27 17:44)