1. Woody owns a carpentry shop that makes tables an chairs. Woody has found that each chair requires 3 board feet of lumber and 2 hours o labor. Each table requires 7 board feet of lumber and 8 hours of labor. His profit on each chair is $15 and his profit on each table is $45. This week, Woody has 420 board feet of lumber and 400 hours of labor available (he doesn't do all the work himseln. He wants to know how many chairs and how many tables he should make to maximize his profit. a) Define the variables that you are going to use for this problem. b) Write the inequalities that represent all of the constraints for Woody's carpentry business. C) Algebraically determine all of the intersection points that are created by the constraints. d) Determine which of the intersection points from part c are the corner points that define the feasible region. e) Write the function that represents the profit function for the business and determine how many tables and chairs should be made in order to maximize the profit.
1. Woody owns a carpentry shop that makes tables an chairs. Woody has found that each chair requires 3 board feet of lumber and 2 hours o labor. Each table requires 7 board feet of lumber and 8 hours of labor. His profit on each chair is $15 and his profit on each table is $45. This week, Woody has 420 board feet of lumber and 400 hours of labor available (he doesn't do all the work himseln. He wants to know how many chairs and how many tables he should make to maximize his profit. a) Define the variables that you are going to use for this problem. b) Write the inequalities that represent all of the constraints for Woody's carpentry business. C) Algebraically determine all of the intersection points that are created by the constraints. d) Determine which of the intersection points from part c are the corner points that define the feasible region. e) Write the function that represents the profit function for the business and determine how many tables and chairs should be made in order to maximize the profit.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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