A furniture maker makes three different style of wardrobes: x, x, and x,. The manufacture of each style of wardrobe requires a certain amount of time in three types of skilled labor: cutting, assembling and painting. Model x, requires 1 hour for the cutting of component parts, 2 hours for assembling and 4 hours for painting. Model x, requires 2 hours for cutting, 4 hours for assembling and painting, respectively. While model x, needs 3, 7 and 5 hours for cutting, assembling and painting accordingly. Currently, 200 cutting hours of component parts, 300 assembling hours and 150 painting hours are available. Determine the product mix that will maximize the furniture maker's revenue if a model x, sells for $20, a painted model x, sells for $30, an unpainted model x, sells for $20 and a model x, sells for $50. (a) Formulate a linear programming model for this problem. (b) Find the optimal solution by using simplex algorithm.
A furniture maker makes three different style of wardrobes: x, x, and x,. The manufacture of each style of wardrobe requires a certain amount of time in three types of skilled labor: cutting, assembling and painting. Model x, requires 1 hour for the cutting of component parts, 2 hours for assembling and 4 hours for painting. Model x, requires 2 hours for cutting, 4 hours for assembling and painting, respectively. While model x, needs 3, 7 and 5 hours for cutting, assembling and painting accordingly. Currently, 200 cutting hours of component parts, 300 assembling hours and 150 painting hours are available. Determine the product mix that will maximize the furniture maker's revenue if a model x, sells for $20, a painted model x, sells for $30, an unpainted model x, sells for $20 and a model x, sells for $50. (a) Formulate a linear programming model for this problem. (b) Find the optimal solution by using simplex algorithm.
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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Transcribed Image Text:A furniture maker makes three different style of wardrobes: x,, x, and x, . The manufacture
of each style of wardrobe requires a certain amount of time in three types of skilled labor:
cutting, assembling and painting. Model x, requires 1 hour for the cutting of component parts,
2 hours for assembling and 4 hours for painting. Model x, requires 2 hours for cutting, 4
hours for assembling and painting, respectively. While model x, needs 3, 7 and 5 hours for
cutting, assembling and painting accordingly. Currently, 200 cutting hours of component
parts, 300 assembling hours and 150 painting hours are available. Determine the product mix
that will maximize the furniture maker's revenue if a model x, sells for $20, a painted model
x, sells for $30, an unpainted model x, sells for $20 and a model x, sells for $50.
(a) Formulate a linear programming model for this problem.
(b) Find the optimal solution by using simplex algorithm.
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