In a specific project, ground water level has to be reduced prior to construction and 3 specific well locations have been chosen. The steady state water level (h) at the most critical point can be expressed as a function of pumpage rates (Q) at these locations. h = 1.0+ (0.7* Q₁ + 1.4 * Q₂ + 1.0 * Q3 ) The cost of each well is composed of an initial cost and operating costs (function of discharge) * COST₁ = 30+12 * Q₁ COST₂ = 45 +10 Q2 COST3 = = 38 + 11 * Q3 Formulate a mathematical program that will determine the optimal (cost efficient) well discharges if maximum pumpage rate is limited to 3 m³/sec for each well and the desired steady state level is 8.0m. (Note: Make sure that no initial cost is applicable for a well with zero discharge).
In a specific project, ground water level has to be reduced prior to construction and 3 specific well locations have been chosen. The steady state water level (h) at the most critical point can be expressed as a function of pumpage rates (Q) at these locations. h = 1.0+ (0.7* Q₁ + 1.4 * Q₂ + 1.0 * Q3 ) The cost of each well is composed of an initial cost and operating costs (function of discharge) * COST₁ = 30+12 * Q₁ COST₂ = 45 +10 Q2 COST3 = = 38 + 11 * Q3 Formulate a mathematical program that will determine the optimal (cost efficient) well discharges if maximum pumpage rate is limited to 3 m³/sec for each well and the desired steady state level is 8.0m. (Note: Make sure that no initial cost is applicable for a well with zero discharge).
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:In a specific project, ground water level has to be reduced prior to construction
and 3 specific well locations have been chosen. The steady state water level
(h) at the most critical point can be expressed as a function of pumpage rates
(Q) at these locations.
h
= 1.0+ (0.7* Q₁ + 1.4 * Q₂ + 1.0 * Q3 )
The cost of each well is composed of an initial cost and operating costs
(function of discharge)
*
COST₁ = 30+12 * Q₁
COST₂ = 45 +10 Q2
COST3 =
= 38 + 11 * Q3
Formulate a mathematical program that will determine the optimal (cost
efficient) well discharges if maximum pumpage rate is limited to 3 m³/sec for
each well and the desired steady state level is 8.0m.
(Note: Make sure that no initial cost is applicable for a well with zero
discharge).
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