1. Woody owns a carpentry shop that makes tabies 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 himself). 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. O Algebraically determine al 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. eWrite 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 tabies 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 himself). 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. O Algebraically determine al 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. eWrite 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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