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문제
A farmer has 100 hectares of agricultural land on which he plans to
grow crops under irrigation using an available water supply of 1 million cubic meters of water per year.
Three types of crops are being considered: soybeans,
wheat, and strawberries. Soybeans require 12,000 m3/ha of water per year, wheat
requires 8,000 m3/ha of water per year, and strawberries require 16,000 m3/ha of
water per year. The cost of water is $0.20/m3
Annual costs of material, equipment, manpower and other expenses (except water) for different crops are (1) soybeans: $4,600/ha; (2) wheat: $2,400/ha;
(3) strawberries: $4,600/ha.
Annual returns for the different crops are (1) soybeans : $15,000/ha; (2) wheat: $10,000/ha; and (3) strawberries: $18,000/ha.
Available market restricts wheat to 75 ha, and strawberries to 10 ha.
질문
1. Formulate a mathematical model to maximize profit, together with their constraints.
2. Find the optimal areas of cultivation for each of the crops using simplex method
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