Explanation Given Information: The provided information is as follows, “Two types of furniture- chairs and sofa is made by a manufacturer. Manufacture of chair requires 6 hours of carpentry, 2 hours of upholstery, and 1 hour of finishing where manufacture of sofa requires 3 hours of carpentry, 6 hours of upholstery, and 1 hour of finishing. The factory has 96 labor-hours for carpentry, 72 labor-hours of upholstery and 18 labor-hours of finishing and the profit per chair is $150 and for sofa $70.” Formula Used: To find the maximum and minimum value of objective function follow the given steps: 1)Translate the linear programming problem into mathematical language and graph the feasible solution set. 3) Determine the vertices of the feasible solution set obtained. 4) Find the value of objective function at each vertex and determine the feasible set. 5) Interpret the result. Addition property: For any real numbers a, b and c, if a = c , then a + b = c + b . Multiplication property: For any real numbers a, b and c ≠ 0 , if a = c , then a ⋅ b = c ⋅ b . Calculation: Make a table according to the given condition as: Chair Sofa Available time Carpenter 6 hours 3 hours At most 96 hours Finishing 1 hour 1 hours at most 18 hours Upholstery 2 hours 6 hours at most 72 hours Profit $150 $70 Let number of chairs be x and number of sofas be y. Then total profit is 150 x + 70 y From the table, For carpentry, the inequality is: 6 x + 3 y ≤ 96 For finishing, the inequality is: x + y ≤ 18 For upholstery, the inequality is: 2 x + 6 y ≤ 72 The inequalities in standard form are: y ≤ − 2 x + 32 y ≤ − x + 18 y ≤ − 1 3 x + 12 x ≥ 0 , y ≥ 0 Assume the inequality as equation to find coordinate pairs. Now to find the intersection point of y = − 2 x + 32 and y = − x + 18 , equate the values of y , − 2 x + 32 = − x + 18 Apply the addition principle and add x on both sides of the equation. − 2 x + 32 = − x + 18 − 2 x + 32 + x = − x + x + 18 − x + 32 = 18 Apply the addition principle and add − 32 on both sides of the equation. − x + 32 = 18 − x + 32 + ( − 32 ) = 18 + ( − 32 ) − x = − 14 x = 14 Put this value x = 14 in y = − x + 18 to get, y = − x + 18 y = − 14 + 18 y = 4 The intersection point is ( 14 , 4 ) . Now to find the intersection of y = − 1 3 x + 12 and y = − x + 18 equate the values of y , − 1 3 x + 12 = − x + 18 Apply the addition principle and add x on both sides of the equation. − 1 3 x + 12 = − x + 18 − 1 3 x + 12 + x = − x + x + 18 − x + 3 x 3 + 12 = 18 2 x 3 + 12 = 18 Apply the addition principle and add − 12 on both sides of the equation

Finite Mathematics & Its Applications Plus Mylab Math With Pearson Etext -- Access Card Package (12th Edition)

12th Edition

ISBN: 9780134464428

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

See similar textbooks

Question

Chapter 3.3, Problem 23E

To determine

To calculate: The maximum profit if the profit per chair is $150 and for sofa $70.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.3, Problem 22E

Chapter 3.3, Problem 24E

Chapter 3 Solutions

Finite Mathematics & Its Applications Plus Mylab Math With Pearson Etext -- Access Card Package (12th Edition)

Ch. 3.1 - Graph the inequality 3xy3.Ch. 3.1 - Graph the feasible set for the system of...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 5-7, solve for x, 2x53 Ch. 3.1 - Prob. 6E Ch. 3.1 - In Exercises 5-7, solve for x, 7. Ch. 3.1 - Which of the following results from solving x+13...

Knowledge Booster

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage