For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic meter of beach sand costs ₽60 and contains 4 units of fine sand, 3 units of coarse sand, and 5 units of gravel. Each cubic meter of river sand costs ₽100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach sand and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables.
i.e:
Max Z = 500x + 300y
Subject to:
4x + 2y <= 60 (1st constraint)
2x + 4y <= 48 (2nd constraint)
x, y >= 0 (non-negativity)
A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic meter of beach sand costs ₽60 and contains 4 units of fine sand, 3 units of coarse sand, and 5 units of gravel. Each cubic meter of river sand costs ₽100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach sand and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.
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