(P5-18)A food distribution company ships fresh
spinach from its four packing plants to large East-Coast cities. The shipping
costs per crate and the supply and demand are shown in the table below.
Formulate a model that will permit the company to
meet its demand at the lowest possible cost.
The company wishes to spread out the source for
each of its markets to the maximum extent possible. To accomplish this, it will
accept a 5% increase in its total transportation cost from part (a). What is
the new transportation plan, and what is the new cost?
MARKETS
Packing Plants
Atlanta
Boston
Charlestown
Dover
Supply
Eaglestown
$6.00
$7.00
$7.50
$7.50
8,000
Farrier
$5.50
$5.50
$4.00
$7.00
10,000
Guyton
$6.00
$5.00
$6.50
$7.00
5,000
Hayesville
$7.00
$7.50
$8.50
$6.50
9,000
Demand
8,000
9,000
10,000
5,000
(P5-32) A security firm needs to connect alarm
systems to the firm’s main control site from five potential trouble locations.
Since the systems must be fail-safe, the cables must be run in special pipes.
These pipes are very expensive but large enough to simultaneously handle five
cables (the maximum that might be needed). Use the minimal-spanning tree model
to find the minimum total length of pipes needed to connect the locations shown
in Figure 5.22. Node 6 represents the main control site.
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