A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of rice and corn to plant. He can make ₽200,000 profit per hectare planted to rice and ₽250,000 profit per hectare planted with corn. However, the corn takes 2 hours of labor per hectare to harvest and the rice takes 1 hour per hectare. The farmer has 8 hours of labor to harvest. To maximize his profit, how many hectares of each should he plant?
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables.
Max Z = 500x + 300y
Subject to:
4x + 2y <= 60 (1st constraint)
2x + 4y <= 48 (2nd constraint)
x, y >= 0 (non-negativity)
A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of rice and corn to plant. He can make ₽200,000 profit per hectare planted to rice and ₽250,000 profit per hectare planted with corn. However, the corn takes 2 hours of labor per hectare to harvest and the rice takes 1 hour per hectare. The farmer has 8 hours of labor to harvest. To maximize his profit, how many hectares of each should he plant?
*additional note: philippine peso is used as currency :)*
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