Question

A furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor. If a chair yields a profit of $65 and a table yields a profit of $90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit?
16 chairs; 24 tables
15 chairs; 18 tables
12 chairs; 28 tables
18 chairs; 20 tables

Answer 1

The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

• 16 chairs; 24 tables
• Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552
• Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608  
• 15 chairs; 18 tables
• Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450
• Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480  
• 12 chairs; 28 tables
• Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564
• Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636  
• 18 chairs; 20 tables
• Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516
• Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544

Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

• 15 x 65 + 18 x 90 = X
• 975 + 1,620 = X
• 2,595 = X

Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

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