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 = 77x106 3700+40 V C₂ The two systems have distinct water conveyance system characteristics. System efficiency parameter (n= Volume delivered) accounts for pipe leak- 1 Volume pumped age and related losses. Given 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 (a) Compute the optimal system configuration (that is, how much wa- ter is withdrawn from each source) to meet the community water needs. (b) A population projection for the year 2025 puts the population of this community at 400. Compute the system configuration to meet the pro- jected demand. (c) Through a conversation and reuse program, the community is able to lower its current per capita water use to 100 gpd. Recompute the system configuration.

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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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 +
System 2: Well-Aquifer
V²
77x106 3700
V
C₂=
V
22000
=
+40
The two systems have distinct water conveyance system characteristics.
System efficiency parameter (n
Volume delivered
Volume pumped
ered) accounts for pipe leak-
age and related losses. Given
710.84
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ter is withdrawn from each source) to meet the community water needs.
(b) A population projection for the year 2025 puts the population of this
community at 400. Compute the system configuration to meet the pro-
jected demand.
1
(c) Through a conversation and reuse program, the community is able to
lower its current per capita water use to 100 gpd. Recompute the system
configuration.
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 + System 2: Well-Aquifer V² 77x106 3700 V C₂= V 22000 = +40 The two systems have distinct water conveyance system characteristics. System efficiency parameter (n Volume delivered Volume pumped ered) accounts for pipe leak- age and related losses. Given 710.84 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. (b) A population projection for the year 2025 puts the population of this community at 400. Compute the system configuration to meet the pro- jected demand. 1 (c) Through a conversation and reuse program, the community is able to lower its current per capita water use to 100 gpd. Recompute the system configuration.
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