A certain objective function is the production function. In utilizing groundwater, we will have a certain number of wells to be utilized for irrigation or domestic uses. The cost of production of water (pumping) usually takes the form:
C = a + pQ + kQ²
Where: a is a constant fixed cost (maintenance), Q is the discharge (MGD), p is the cost usually directly proportional to flow rate and k is the constant which depends on (friction f, topography, pipe size, roughness e). By increasing the number of wells and increasing the supply, we will have the well field, (N wells) then we may have M. Design criteria (maximum discharge Q at minimum cost C).
For the above equation suppose you have:
a = 13, p = 4, k = 1, C = cost in $/day, Q = million gallon/day(MGD) (2 ≤ Q ≤ 5).
Analyze the economy of the production of water. Check three methods:
a. Analytical method
b. Lagrange method
c. Graphical method.