The city of Lancaster’s water distribution system12 has 3 wells for water supply. There are 10 pumps at these 3 wells. It is estimated that a pumping 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:

Pump Maximum

(gal/min)

Cost

($/gal/min)

From Well 1 1100 0.05 1 2 1100 0.05 2 3 1100 0.05 3 4 1500 0.07 1 5 1500 0.07 2 6 1500 0.07 3 7 2500 0.13 1 8 2500 0.13 2 9 2500 0.13 3 10 2500 0.13 3 Lancaster wishes to determine the least cost way to meet its pumping needs.

(a) Explain why appropriate decision variables for a model of this problem are 1j = 1,c, 102 xj!pump rate per minute of pump j

(b) Assign suitable symbolic names to the constants of the cost and maximum rate values in the table above.

(c) Formulate an objective function to minimize the cost of the pumping plan selected.

(d) Formulate a system of 3 constraints enforcing well capacities.

(e) Formulate a system of 10 constraints enforcing pump capacities.

(f) Formulate a single constraint enforcing the overall pumping requirement.
(g) Complete your model with an appropriate system of variable-type constraints.
(h) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective? Explain.
(i) Enter and solve your model with class optimization software.