Formulate system of 3 constraints enforcing well capacities

Assignment Help Civil Engineering
Reference no: EM13315128

The city of Lancaster's water distribution system has 3 wells for water supply. There are 10 pumps at these 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 and 7000 gal/min from Well 3. There are also di erent 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 variables for a model of this problem are (j = 1; : : : ; 10) xj = pump rate per minute of pump j 5

(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 classi?ed as an LP, NLP, ILP or INLP? Is it single or multi-objective? (i) (OPTIONAL) Solve this problem using GAMS

What is the maximum deceleration possible

The car of Prob. 3/59 is traveling at 25 mi/hr when the driver applies the brakes, and the car continues to move along the circular path. What is the maximum deceleration po

What types of construction are you permitted

What is the required re resistance rating for the walls around the elevator shafts? For the purposes of this exercise, when referring to Figure 22.7, assume the highest rati

How long will it take alexis to pay off the loan

how long (how many monthly payments) will it take Alexis to pay off the loan and accrued interest completely (to a zero balance). Use linear interpolation as necessary to ge

Calculate the natural rate of groundwater discharge through

Given a potentiometric surface with a regional slope of 7m/km, calculate the natural rate of groundwater discharge through a confined aquifer with transmissivity (hydraulic co

Determine the magnitude of force p to produce

A thin-walled cylindrical tank of radius r is subjected simultaneously to internal pressure p and a compressive force P through rigid end plates. Determine the magnitude of

Determine the flow rate of the oil

Oil of a specific gravity of 0.75 is flowing through a 6-in pipe under a pressure of 15 psi. If the total energy relative to the datumplate is 8.0 ft below the center of the

Determine the required dimensions of a hollow steel shaft

Determine the required dimensions. The inside diameter is to be two- thirds of the outside diameter. The allowable shearing stress is 70 MPa, and the angle of twist is not t

Develop equation that determines mass of finishing rods

When in use, a fishing rod can be approximated to act as a cantilevered beam. Assume that the force (P) is applied to the end of the beam by a fish while the fisherman rigid

Write a Review 