A river supplies water to an industrial complex and agricultural lands located downstream of the complex. The average monthly industrial and irrigation demands and the monthly river flows in a dry year are given in Table 8. 21 (numbers are in million cubic meters). The prices of water for industrial and irrigation uses are $80,000 and $9,000 per million cubic meters. i. Formulate the problem for optimizing the water allocation from this river. ii. Solve the problem using linear programming.

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TABLE 8.21 Average Monthly Industrial and Irrigation Demands and the Monthly River Flows in a Dry Year of Problem 4 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Industrial demand 8 8.5 8.5 9 9 9.5 9.5 10 9.5 9 8.5 8.5 Irrigation demand 0 0 201 50 55 70 70 65 20 10 0 0 Flow 22.5 24.3 36 43.2 54 37.8 22.5 15.3 12.6 16.2 18 22.5