Question: E. Solve the following problems .Show your step - by-step soiution Is. 1. A farmer has 40 hectares of farm on which to plan rice

E. Solve the following problems .Show your step - by-step soiution Is. 1. A farmer has 40 hectares of farm on which to plan rice and corn. The rice needs 4 units of insecticides and 2 units of fertilizer per hectare, while corn requires 3 units of insecticides and 6 units of fertilizer. He has at least 90 units of insecticides and at least 120 units of fertilizer available. His average profit per hectare on rice is P15.000 and P10,000 on corn. How many hectares of each crop should he plant to maximize his average profit ? 2. Solve by the simplex method by filling up the subsequent tables : Maximize :100x + 80y New Program Subject to: 4x+2y5100 2 x+4y$140 x20;y20 0 Prod (Solution (Solution 5 2 Table I Variables) Values) 0 (Solution (Solution 5 2 Variables) Values) Table II 0 (Solution (Solution 5 2 Table III Variables) Values) Decision 3. Minimize : Z = Minimize : 30 x"' 40 y Subject to: 4x+2y332 x+ 3y 5 13 x20;y20 " The essence of Mathematics is not to make simple things complicated but to make complicated things simple " - S. Guddler "

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