Engineering Optimization: Theory and Practice, Fourth Edition

Problems 161

Figure 3.16 Reservoir in an irrigation district.

wet and dry seasons, respectively. Of the total amount of water released to the irrigation

district per year(x 2 ), 30% is to be released during the wet season and 70% during the

dry season. The yearly cost of diverting the required amount of water from the main

stream to the irrigation district is given by 18( 0. 3 x 2 )+ 12 ( 0. 7 x 2 ). The cost of building

and maintaining the reservoir, reduced to an yearly basis, is given by 25x 1. Determine

the values ofx 1 andx 2 to minimize the total yearly cost.

3.5 Solve the following system of equations using pivot operations:

4 x 1 − 7 x 2 + 2 x 3 = − 8

3 x 1 + 4 x 2 − 5 x 3 = − 8

5 x 1 +x 2 − 8 x 3 = − 34