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2-28 The city of Lancaster's water distribution system has 3 wells for water supply. There are 10 12 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: Maximum Cost From Pump (gal/min) ($/gal/min) 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 vari- ables for a model of this problem are (j = 1, 10) 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- (i) Enter and solve your model with class ate system of variable-type constraints. optimization software.

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