A furniture company makes bar stools, tables, and chairs

MATLAB: An Introduction with Applications
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A furniture company makes bar stools, tables, and chairs

HW16: Problem 1
Previous Problem Problem List Next Problem
t) A furniture company makes bar stools, tables, and chairs. Each bar stool requires 1 hour of labor. 8 feet of wood, and 0.2 gallons of stain. Each
chair requires 4 hours of labor, 16 feet of wood, and 0.4 gallons of stain. Each table requires 2 hours of labor, 32 feet of wood, and 0.5 gallons of stain.
Each week, the company has 700 hours of labor, 3360 feet of wood, and 60 gallons of stain. The company makes $10 in profit per bar stool, $25 in profit
per chair, and $35 in profit per table. In order to maximize their profit, the furniture company should make
bar stools per week,
This strategy will leave
chairs per week,
What is the maximal profit?
and
tables per week.
unused hours of labor per week,
unused feet of wood per week,
gallons of stain per week
SUGGESTION: Let x denote number of bar stools, y denote the number of chairs, and z denote the number of tables. Write down a system of
inequalities. Introduce slack variables and build a simplex tableau. Then use the simplex algorithm to determine the optimal solution, along with the
maximal profit and the amounts of the unused resources.
Transcribed Image Text:HW16: Problem 1 Previous Problem Problem List Next Problem t) A furniture company makes bar stools, tables, and chairs. Each bar stool requires 1 hour of labor. 8 feet of wood, and 0.2 gallons of stain. Each chair requires 4 hours of labor, 16 feet of wood, and 0.4 gallons of stain. Each table requires 2 hours of labor, 32 feet of wood, and 0.5 gallons of stain. Each week, the company has 700 hours of labor, 3360 feet of wood, and 60 gallons of stain. The company makes $10 in profit per bar stool, $25 in profit per chair, and $35 in profit per table. In order to maximize their profit, the furniture company should make bar stools per week, This strategy will leave chairs per week, What is the maximal profit? and tables per week. unused hours of labor per week, unused feet of wood per week, gallons of stain per week SUGGESTION: Let x denote number of bar stools, y denote the number of chairs, and z denote the number of tables. Write down a system of inequalities. Introduce slack variables and build a simplex tableau. Then use the simplex algorithm to determine the optimal solution, along with the maximal profit and the amounts of the unused resources.
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