A community of 300 residents (water use per person = 130 gpd) is looking at using two sources for water supply: 1. Nearby lake, 2. Local well- aquifer system. The cost functions are as follows (C₁ and C₂ represent costs are in arbitrary monetary units and V is the volume of water pumped per day, in gallons): Cost Functions: System 1: Lake C₁ = 410 + V 22000 System 2: Well-Aquifer V² C₂ C2= 77x106 V 3700 +40 The two systems have distinct water conveyance system characteristics. System efficiency parameter (n = Volume delivered) accounts for pipe leak- age and related losses. Given pumped 7₁=0.84 72 = 0.92 In all computations, the goal is to minimize total cost. (a) Compute the optimal system configuration (that is, how much wa- ter is withdrawn from each source) to meet the community water needs.
A community of 300 residents (water use per person = 130 gpd) is looking at using two sources for water supply: 1. Nearby lake, 2. Local well- aquifer system. The cost functions are as follows (C₁ and C₂ represent costs are in arbitrary monetary units and V is the volume of water pumped per day, in gallons): Cost Functions: System 1: Lake C₁ = 410 + V 22000 System 2: Well-Aquifer V² C₂ C2= 77x106 V 3700 +40 The two systems have distinct water conveyance system characteristics. System efficiency parameter (n = Volume delivered) accounts for pipe leak- age and related losses. Given pumped 7₁=0.84 72 = 0.92 In all computations, the goal is to minimize total cost. (a) Compute the optimal system configuration (that is, how much wa- ter is withdrawn from each source) to meet the community water needs.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A community of 300 residents (water use per person = 130 gpd) is looking
at using two sources for water supply: 1. Nearby lake, 2. Local well-
aquifer system. The cost functions are as follows (C₁ and C₂ represent
costs are in arbitrary monetary units and V is the volume of water pumped
per day, in gallons):
Cost Functions:
System 1: Lake
C₁ = 410 +
V
22000
System 2: Well-Aquifer
V²
V
C2= 77x106
+40
3700
-
The two systems have distinct water conveyance system characteristics.
System efficiency parameter (n = Volume delivered) accounts for pipe leak-
age and related losses. Given
pumped
7₁=0.84
72 = 0.92
In all computations, the goal is to minimize total cost.
(a) Compute the optimal system configuration (that is, how much wa-
ter is withdrawn from each source) to meet the community water needs.
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