2-28 The city of Lancaster's water distribution
system has 3 wells for water supply. There are 10
pumps at these 3 wells. It is estimated that a pump-
ing rate of 10,000 gallons per minute is needed to
satisfy the city's total water demand. There are
limits on how much water can be pumped from
each well: 3000 gal/min from well 1; 2500 gal/min
from well 2; 7000 gal/min from well 3. There are
also different costs of operating each pump and
limits on the rate of each pump:
Lancaster wishes to determine the least cost way
to meet its pumping needs.
(a) Explain why appropriate decision vari-
ables for a model of this problem are
(j = 1,
X, 11 pump rate per minute of pump j
(b) Assign suitable symbolic names to the
constants of the cost and maximum rate
(c) Formulate an objective function to mini-
values in the table above.
mize the cost of the pumping plan selected.
(d) Formulate a system of 3 constraints en-
(e) Formulate a system of 10 constraints en-
forcing well capacities.
forcing pump capacities.
(h) Is your model best classified as an LP, an
NLP, an ILP, or an INLP, and is it single-
(f) Formulate a single constraint enforcing
or multiobjective? Explain.
the overall pumping requirement.
(g) Complete your model with an appropri-
Enter and solve your model with class
ate system of variable-type constraints.
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