HW5 - Florida International University Department of Civil...

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Unformatted text preview: Florida International University Department of Civil and Environmental Engineering EGN5455 – Numerical Methods in Engineering Assignment No. 5 – Due 29 Oct 2008 (1) Find a numerical solution to the nonlinear optimization problem for irrigation (water and salinity) discussed in class, to find the values of irrigation volume (x1) and salinity (x2) to maximize profits. Use the following parameters (in consistent units): c = P = Y0 = QY = d = Smax = 1. Verify the positive definiteness condition by finding the two eigenvalues of the second partial differential matrix of the problem at (x1,x2)*. (2) Maximize the revenue obtained by a farmer on a combination of two crops, given constraints in available land and water, and on minimum total crop grown. The formulation of the problem is as follows: Max {6 x1 + 11 x2} Subject to: Water constraint: Land constraint: Minimum total crop constraint: Non‐negativity of Crop 1: Non‐negativity of Crop 2: 2 x1 + x2 ≤ 104 x1 + 2 x2 ≤ 76 x1 + x2 ≥ 25 x1 ≥ 0 x2 ≥ 0 ...
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