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AMBK Company manufactures furniture such as sofas and tables. In their current inven- tory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of P hundred pesos where P(x, y) = 12xy for selling a units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit? (Use the Lagrange method of optimization.)

AMBK Company manufactures furniture such as sofas and tables. In their current inven- tory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of P hundred pesos where P(x, y) = 12xy for selling a units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit? (Use the Lagrange method of optimization.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. AMBK Company manufactures furniture such as sofas and tables. In their current inven- tory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of hundred pesos where P(x, y) = 12xy for selling a units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit? (Use the Lagrange method of optimization.)
Transcribed Image Text:2. AMBK Company manufactures furniture such as sofas and tables. In their current inven- tory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of hundred pesos where P(x, y) = 12xy for selling a units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit? (Use the Lagrange method of optimization.)
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