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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 56E
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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.
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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