(a) To determine To calculate: The number of bicycles to maximize the profit if the three models of bicycles 1-, 3- and 10-speed are made both aluminum and steel. The units available of steel is 91800 and the aluminum is 42000 units. These three models of bicycles required 20 , 30 & 40 units of steel and 12 , 21 & 16 units of aluminum. If the maximum profit makes $8 per 1-speed bicycle, $12 per 3-speed bicycle and $24 per 10-speed bicycle. Explanation Given: The three models of bicycles 1-, 3- and 10-speed are made both aluminum and steel. The units available of steel is 91800 and the aluminum is 42000 units. These three models of bicycles required 20 , 30 & 40 units of steel and 12 , 21 & 16 units of aluminum. If the maximum profit makes $8 per 1-speed bicycle, $12 per 3-speed bicycle and $24 per 10-speed bicycle. Formula used: Locate the pivot column by finding the most negative indicator in the last row. Then, locate the pivot row by computing the necessary quotients and finding the smallest one. Calculation: Suppose x 1 is the number of 1-Speed bicycles, x 2 is the number of 3-Speed bicycles, x 3 is the number of 10-Speed bicycles and z is the total profit. Consider the summarize the information as follows, Aluminium Steel Profit 1 Speed 12 20 $ 8 2 Speed 21 30 $ 12 3 Speed 16 40 $ 24 Amount Available 42000 91800 The constraints can be expressed as: 20 x 1 + 30 x 2 + 40 x 3 ≤ 91800 12 x 1 + 21 x 2 + 16 x 3 ≤ 42000 Where x 1 , x 2 and x 3 are all nonnegative. The first of these constrains says that 20 x 1 + 30 x 2 + 40 x 3 is less than or perhaps equal to 91800. Suppose s 1 is the slack variable, Therefore, the first equation is, 20 x 1 + 30 x 2 + 40 x 3 + s 1 = 91800 The second constrains 12 x 1 + 21 x 2 + 16 x 3 ≤ 42000 can be expressed by adding slack variable s 2 . Therefore, the second equation is, 12 x 1 + 21 x 2 + 16 x 3 + s 2 = 42000 The company makes profit, $8 per 1-speed bike, and $12 per 3-speed bicycle and $24 per 10-speed. Therefore, the total profit is, z = Profit on 1-Speed bicycles + profit on 2-Speed bicycles + profit on 3-Speed bicycles Therefore, z = 8 x 1 + 12 x 2 + 24 x 3 After simplification, − 8 x 1 − 12 x 2 − 24 x 3 + z = 0 Now linear programming problem can be written as follows, Maximize z = 8 x 1 + 12 x 2 + 24 x 3 Subject to 20 x 1 + 30 x 2 + 40 x 3 + s 1 = 91800 12 x 1 + 21 x 2 + 16 x 3 + s 2 = 42000 With x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 Thus, the in (b) To determine To calculate: The value of slack variable from the linear programming table that is provided below. x 1 x 2 x 3 s 1 s 2 [ .50 .75 1 1 40 0 2295 4 9 0 − 2 5 1 5280 4 6 0 3 5 0 55080 ]

Mathematics with Applications In the Management, Natural, and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (11th Edition)

11th Edition

ISBN: 9780321935441

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 7.5, Problem 5E

(a)

To determine

To calculate: The number of bicycles to maximize the profit if the three models of bicycles 1-, 3- and 10-speed are made both aluminum and steel. The units available of steel is 91800 and the aluminum is 42000 units. These three models of bicycles required 20,30&40 units of steel and 12,21&16 units of aluminum. If the maximum profit makes $8 per 1-speed bicycle, $12 per 3-speed bicycle and $24 per 10-speed bicycle.

(b)

To determine

To calculate: The value of slack variable from the linear programming table that is provided below.

x1 x2x3 s1 s2[.50.75114002295490−251528046035055080]

Expert Solution & Answer

Chapter 7 Solutions

Mathematics with Applications In the Management, Natural, and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (11th Edition)

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

Ch. 7.1 - Prob. 4E Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 9E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 11E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 17E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 19E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 32E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 34E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 40E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 43E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - 52. Business A manufacturer of electric shavers...Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.2 - Checkpoint 1 Suppose the objective function in...Ch. 7.2 - Prob. 2CP Ch. 7.2 - Prob. 3CP Ch. 7.2 - Checkpoint 4 Use the region of feasible solutions...Ch. 7.2 - Prob. 5CP Ch. 7.2 - Prob. 6CP Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Prob. 6E Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Prob. 9E Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Prob. 17E Ch. 7.2 - 18. Find values and that maximize subject to...Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.3 - Prob. 1CP Ch. 7.3 - Prob. 2CP Ch. 7.3 - Prob. 3CP Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Write the constraints in Exercises 1–4 as linear...Ch. 7.3 - Prob. 5E Ch. 7.3 - Solve these linear programming problems, which are...Ch. 7.3 - Prob. 7E Ch. 7.3 - Solve these linear programming problems, which are...Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Solve these linear programming problems, which are...Ch. 7.3 - Prob. 13E Ch. 7.3 - Solve the following linear programming problems....Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Solve the following linear programming problems....Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.4 - Prob. 1CP Ch. 7.4 - Prob. 2CP Ch. 7.4 - Prob. 3CP Ch. 7.4 - Prob. 4CP Ch. 7.4 - Prob. 5CP Ch. 7.4 - Prob. 6CP Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - In Exercises 1–4, (a) determine the number of...Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Prob. 34E Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.5 - Prob. 1CP Ch. 7.5 - Prob. 1E Ch. 7.5 - Prob. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - Set up the initial simplex tableau for each of the...Ch. 7.5 - In each of the given exercises, (a) use the...Ch. 7.5 - In each of the given exercises, (a) use the...Ch. 7.5 - In each of the given exercises, (a) use the...Ch. 7.5 - Prob. 8E Ch. 7.5 - Prob. 9E Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.5 - Prob. 21E Ch. 7.5 - Prob. 22E Ch. 7.6 - Checkpoint 1 Give the transpose of each...Ch. 7.6 - Prob. 2CP Ch. 7.6 - Prob. 3CP Ch. 7.6 - Prob. 4CP Ch. 7.6 - Prob. 5CP Ch. 7.6 - Prob. 6CP Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7.6 - Prob. 13E Ch. 7.6 - Prob. 14E Ch. 7.6 - Prob. 15E Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 19E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - 28. Business An animal food must provide at least...Ch. 7.6 - Prob. 29E Ch. 7.6 - 30. Business Joan McKee has a part-time job...Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.7 - Prob. 1CP Ch. 7.7 - Prob. 2CP Ch. 7.7 - Prob. 3CP Ch. 7.7 - Prob. 4CP Ch. 7.7 - Prob. 5CP Ch. 7.7 - Prob. 1E Ch. 7.7 - Prob. 2E Ch. 7.7 - Prob. 3E Ch. 7.7 - Prob. 4E Ch. 7.7 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Use the two-stage method to solve Exercises 33–40....Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7 - Prob. 1CE Ch. 7 - 2. Consider preparing a stir-fry using beef, oil,...Ch. 7 - Prob. EP Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Graph each of the given linear inequalities. 3. Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Use the graphical method to solve Exercises...Ch. 7 - Use the graphical method to solve Exercises...Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - 19. Finance The BlackRock Equity Dividend Fund...Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - 37. When is it necessary to use the simplex method...Ch. 7 - Prob. 38RE Ch. 7 - 39. What kind of problem can be solved with the...Ch. 7 - 40. In solving a linear programming problem, you...Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Use the method of duals to solve these...Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Use the two-stage method to solve these...Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Business Solve the following maximization...Ch. 7 - Prob. 58RE Ch. 7 - Business Solve the following maximization...Ch. 7 - Prob. 60RE Ch. 7 - Prob. 61RE Ch. 7 - Business Solve the following minimization...Ch. 7 - Business Solve these mixed-constraint...Ch. 7 - Business Solve these mixed-constraint...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Calculus Volume 1
Math
ISBN:9781938168024
Author:Strang, Gilbert
Publisher:OpenStax College
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education

Discrete Mathematics and Its Applications ( 8th I...

Math

ISBN:9781259676512

Author:Kenneth H Rosen

Publisher:McGraw-Hill Education

Mathematics for Elementary Teachers with Activiti...

Math

ISBN:9780134392790

Author:Beckmann, Sybilla

Publisher:PEARSON

Calculus Volume 1

Math

ISBN:9781938168024

Author:Strang, Gilbert

Publisher:OpenStax College

Thinking Mathematically (7th Edition)

Math

ISBN:9780134683713

Author:Robert F. Blitzer

Publisher:PEARSON

Discrete Mathematics With Applications

Math

ISBN:9781337694193

Author:EPP, Susanna S.

Publisher:Cengage Learning,

Pathways To Math Literacy (looseleaf)

Math

ISBN:9781259985607

Author:David Sobecki Professor, Brian A. Mercer

Publisher:McGraw-Hill Education

SEE MORE TEXTBOOKS

Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY

Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY

Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY

Videos

To calculate: The value of slack variable from the linear programming table that is provided below. x1 x2x3 s1 s2[.50.75114002295490−251528046035055080]

Chapter 7 Solutions

To calculate: The value of slack variable from the linear programming table that is provided below.

x1 x2x3 s1 s2[.50.75114002295490−251528046035055080]