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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042
BuyFind

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042

Solutions

Chapter 4.4, Problem 4E
Textbook Problem

In Problems 1-4, complete the following.

(a) Form the matrix associated with each given minimization problem and find its transpose.

(b) Write the dual maximization problem. Be sure to rename the variables.

Minimize g = 9 y 1 + 10 y 2 subject to

y 1 + 2 y 2 21 3 y 1 + 2 y 2 27

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Chapter 4 Solutions

Mathematical Applications for the Management, Life, and Social Sciences
Ch. 4.1 - In Problems 7-12, the graph of the boundary...Ch. 4.1 - In Problems 7-12, the graph of the boundary...Ch. 4.1 - In Problems 7-12, the graph of the boundary...Ch. 4.1 - In Problems 7-12, the graph of the boundary...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - 27. Management The Wellbuilt Company produces two...Ch. 4.1 - Learning environments An experiment that involves...Ch. 4.1 - 29. Manufacturing A company manufactures two types...Ch. 4.1 - 30. Manufacturing Sierra Wood Products...Ch. 4.1 - 31. Advertising Apex Motors manufactures luxury...Ch. 4.1 - Manufacturing The Video Star Company makes two...Ch. 4.1 - 33. Politics A candidate wants to use a...Ch. 4.1 - 34. Nutrition In a hospital ward, the patients can...Ch. 4.1 - 35. Manufacturing A sausage company makes two...Ch. 4.1 - 36. Manufacturing A cereal manufacturer makes two...Ch. 4.2 - 1. Find the maximum and minimum values of the...Ch. 4.2 - 2. Find the maximum and minimum values (if they...Ch. 4.2 - In Problems 1-4, use the given feasible region...Ch. 4.2 - In Problems 1-4, use the given feasible region...Ch. 4.2 - In Problems 1-4, use the given feasible region...Ch. 4.2 - In Problems 1-4, use the given feasible region...Ch. 4.2 - In Problems 5-8, the graph of the feasible region...Ch. 4.2 - In Problems 5-8, the graph of the feasible region...Ch. 4.2 - In Problems 5-8, the graph of the feasible region...Ch. 4.2 - In Problems 5-8, the graph of the feasible region...Ch. 4.2 - In Problems 9-12, find the indicated maximum or...Ch. 4.2 - In Problems 9-12, find the indicated maximum or...Ch. 4.2 - In Problems 9-12, find the indicated maximum or...Ch. 4.2 - In Problems 9-12, find the indicated maximum or...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - 25. Manufacturing The Wellbuilt Company produces...Ch. 4.2 - Learning environments An experiment involving...Ch. 4.2 - 27. Manufacturing A company manufactures two types...Ch. 4.2 - 28. Manufacturing Sierra Wood Products...Ch. 4.2 - 29. Politics A candidate wants to use a...Ch. 4.2 - 30. Nutrition In a hospital ward, the patients can...Ch. 4.2 - 31. Production scheduling Newjet, Inc....Ch. 4.2 - 32. Production scheduling At one of its factories,...Ch. 4.2 - 33. Nutrition A privately owned lake contains two...Ch. 4.2 - 34. Nutrition In a zoo, there is a natural habitat...Ch. 4.2 - Shadow prices—land management For Problems 35 and...Ch. 4.2 - Shadow prices—land management For Problems 35 and...Ch. 4.2 - 37. Manufacturing Two factories produce three...Ch. 4.2 - 38. Nutrition In a laboratory experiment, two...Ch. 4.2 - 39. Manufacturing The Janie Gioffre Drapery...Ch. 4.2 - 40. Nutrition Two foods contain proteins,...Ch. 4.2 - 41. Manufacturing A sausage company makes two...Ch. 4.2 - 42. Manufacturing A cereal manufacturer makes two...Ch. 4.2 - 43. Shipping costs TV Circuit has 30 large-screen...Ch. 4.2 - 44. Construction A contractor builds two types of...Ch. 4.2 - Management A bank has two types of branches. A...Ch. 4.2 - 46. Manufacturing A company manufactures two...Ch. 4.3 - 1. Write the following constraints as equations by...Ch. 4.3 - 2. Set up the simplex matrix to maximize subject...Ch. 4.3 - Using the simplex matrix from Problem 2, perform...Ch. 4.3 - Using the simplex matrix from Problem 2, perform...Ch. 4.3 - Using the simplex matrix from Problem 2, perform...Ch. 4.3 - Using the simplex matrix from Problem 2, perform...Ch. 4.3 - 1. Convert the constraint inequalities to...Ch. 4.3 - 2. Convert the constraint inequalities to...Ch. 4.3 - In Problems 3-6, set up the simplex matrix used to...Ch. 4.3 - In Problems 3-6, set up the simplex matrix used to...Ch. 4.3 - In Problems 3-6, set up the simplex matrix used to...Ch. 4.3 - In Problems 3-6, set up the simplex matrix used to...Ch. 4.3 - In Problems 7-10, a simplex matrix is given in...Ch. 4.3 - In Problems 7-10, a simplex matrix is given in...Ch. 4.3 - In Problems 7-10, a simplex matrix is given in...Ch. 4.3 - In Problems 7-10, a simplex matrix is given in...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - In Problems 19-26, use the simplex method to...Ch. 4.3 - 27. Maximize subject to Ch. 4.3 - 28. Maximize subject to Ch. 4.3 - In Problems 27-30, use Excel to solve each linear...Ch. 4.3 - In Problems 27-30, use Excel to solve each linear...Ch. 4.3 - Problems 31-38 involve linear programming problems...Ch. 4.3 - Problems 31-38 involve linear programming problems...Ch. 4.3 - Problems 31-38 involve linear programming problems...Ch. 4.3 - Problems 31-38 involve linear programming problems...Ch. 4.3 - In Problems 35-38, use the simplex method to...Ch. 4.3 - In Problems 35-38, use the simplex method to...Ch. 4.3 - In Problems 35-38, use the simplex method to...Ch. 4.3 - In Problems 35-38, use the simplex method to...Ch. 4.3 - Manufacturing Newjet Inc. manufactures two types...Ch. 4.3 - 40. Construction A contractor builds two types of...Ch. 4.3 - Production scheduling At one of its factories, a...Ch. 4.3 - 42. Budget utilization A car rental agency has a...Ch. 4.3 - 43. Production scheduling Happy Valley Ice Cream...Ch. 4.3 - 44. Experimentation An experiment involves placing...Ch. 4.3 - Problems 45-48 involve three variables. Solve them...Ch. 4.3 - Problems 45-48 involve three variables. Solve...Ch. 4.3 - Problems 45-48 involve three variables. Solve...Ch. 4.3 - Problems 45-48 involve three variables. Solve...Ch. 4.3 - In Problems 49-54, use Excel to solve each linear...Ch. 4.3 - In Problems 49-54, use Excel to solve each linear...Ch. 4.3 - In Problems 49-54, use Excel to solve each linear...Ch. 4.3 - In Problems 49-54, use Excel to solve each linear...Ch. 4.3 - In Problems 49-54, use Excel to solve each linear...Ch. 4.3 - In Problems 49-54, use Excel to solve each linear...Ch. 4.4 - Perform the following steps to begin the process...Ch. 4.4 - Perform the following steps to begin the process...Ch. 4.4 - Perform the following steps to begin the process...Ch. 4.4 - Perform the following steps to begin the process...Ch. 4.4 - Perform the following steps to begin the process...Ch. 4.4 - In Problems 1-4, complete the following. (a) Form...Ch. 4.4 - In Problems 1-4, complete the following. (a) Form...Ch. 4.4 - In Problems 1-4, complete the following. (a) Form...Ch. 4.4 - In Problems 1-4, complete the following. (a) Form...Ch. 4.4 - In Problems 5 and 6, suppose a primal minimization...Ch. 4.4 - In Problems 5 and 6, suppose a primal minimization...Ch. 4.4 - In Problems 7-10, write the dual maximization...Ch. 4.4 - In Problems 7-10, write the dual maximization...Ch. 4.4 - In Problems 7-10, write the dual maximization...Ch. 4.4 - In Problems 7-10, write the dual maximization...Ch. 4.4 - Use the simplex method in Problems 11-14. 11....Ch. 4.4 - Use the simplex method in Problems 11-14. 12....Ch. 4.4 - Use the simplex method in Problems 11-14. 13....Ch. 4.4 - Use the simplex method in Problems 11-14. 14....Ch. 4.4 - In Problems 15 and 16, a primal maximization...Ch. 4.4 - In Problems 15 and 16, a primal maximization...Ch. 4.4 - In Problems 17-20, use Excel or some other...Ch. 4.4 - In Problems 17-20, use Excel or some other...Ch. 4.4 - In Problems 17-20, use Excel or some other...Ch. 4.4 - In Problems 17-20, use Excel or some other...Ch. 4.4 - 21. Production scheduling CDF Appliances has...Ch. 4.4 - Manufacturing Nekita Corporation assembles cell...Ch. 4.4 - Manufacturing The Video Star Company makes two...Ch. 4.4 - 24. Nutrition A pork producer is considering two...Ch. 4.4 - 25. Production A small company produces two...Ch. 4.4 - 26. Nutrition In a hospital ward, the patients can...Ch. 4.4 - 27. Production Two factories produce three...Ch. 4.4 - 28. Nutrition In a laboratory experiment, two...Ch. 4.4 - 29. Politics A political candidate wants to use a...Ch. 4.4 - 30. Production The James MacGregor Mining Company...Ch. 4.4 - In Problems 31-36, use the simplex method, Excel,...Ch. 4.4 - In Problems 31-36, use the simplex method, Excel,...Ch. 4.4 - In Problems 31-36, use the simplex method, Excel,...Ch. 4.4 - In Problems 31-36, use the simplex method, Excel,...Ch. 4.5 - 1. Write the simplex matrix to maximize subject...Ch. 4.5 - 2. Using the matrix from Problem 1, find the...Ch. 4.5 - In Problems 1-4, express each inequality as a ...Ch. 4.5 - In Problems 1-4, express each inequality as a ...Ch. 4.5 - In Problems 1-4, express each inequality as a ...Ch. 4.5 - In Problems 1-4, express each inequality as a ...Ch. 4.5 - In Problems 5-8, complete both of the...Ch. 4.5 - In Problems 5-8, complete both of the...Ch. 4.5 - In Problems 5-8, complete both of the...Ch. 4.5 - In Problems 5-8, complete both of the...Ch. 4.5 - In Problems 9 and 10, a final simplex matrix for a...Ch. 4.5 - In Problems 9 and 10, a final simplex matrix for a...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 11-18, use the simplex method to find...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - Problems 27-30 involve maximization with mixed...Ch. 4.5 - Problems 27-30 involve maximization with mixed...Ch. 4.5 - Problems 27-30 involve maximization with mixed...Ch. 4.5 - Problems 27-30 involve maximization with mixed...Ch. 4.5 - Problems 31-36 involve minimization with mixed...Ch. 4.5 - Problems 31-36 involve minimization with mixed...Ch. 4.5 - Problems 31-36 involve minimization with mixed...Ch. 4.5 - Problems 31-36 involve minimization with mixed...Ch. 4.5 - Problems 31-36 involve minimization with mixed...Ch. 4.5 - Problems 31-36 involve minimization with mixed...Ch. 4.5 - In Problems 37 and 38, use Excel or some other...Ch. 4.5 - Land management A farm co-op has two farms, one at...Ch. 4 - In Problems 1-4, use the given feasible region...Ch. 4 - In Problems 1-4, graph the solution set of each...Ch. 4 - In Problems 1-4, graph the solution set of each...Ch. 4 - In Problems 1-4, graph the solution set of each...Ch. 4 - In Problems 5-8, a function and the graph of a...Ch. 4 - In Problems 5-8, a function and the graph of a...Ch. 4 - In Problems 5-8, a function and the graph of a...Ch. 4 - In Problems 5-8, a function and the graph of a...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - In Problems 16-19, use the simplex method to solve...Ch. 4 - In Problems 16-19, use the simplex method to solve...Ch. 4 - In Problems 16-19, use the simplex method to solve...Ch. 4 - In Problems 16-19, use the simplex method to solve...Ch. 4 - Problems 20 and 21 have nonunique solutions. If...Ch. 4 - Problems 20 and 21 have nonunique solutions. If...Ch. 4 - In Problems 22-25, form the dual and use the...Ch. 4 - In Problems 22-25, form the dual and use the...Ch. 4 - In Problems 22-25, form the dual and use the...Ch. 4 - In Problems 22-25, form the dual and use the...Ch. 4 - Problems 26 and 27 involve mixed constraints....Ch. 4 - Problems 26 and 27 involve mixed constraints....Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - 36. Manufacturing A company manufactures backyard...Ch. 4 - 37. Production A company produces two different...Ch. 4 - 38. Manufacturing Chairco manufactures two types...Ch. 4 - 39. Production A small industry produces two...Ch. 4 - 40. Production Pinocchio Crafts makes two types of...Ch. 4 - Profit At its Jacksonville factory, Nolmaur...Ch. 4 - 42. Nutrition A nutritionist wants to find the...Ch. 4 - 43. Nutrition A laboratory technician wants to...Ch. 4 - 44. Production A company makes three products (I,...Ch. 4 - 45. Profit A company makes pancake mix and cake...Ch. 4 - 46. Manufacturing A company manufactures desks and...Ch. 4 - 47. Cost Armstrong Industries makes two different...Ch. 4 - 1. Maximize subject to the constraints determined...Ch. 4 - 2. Following are three simplex matrices in various...Ch. 4 - 3. Graph the solution region for each of the...Ch. 4 - 4. Formulate the dual maximization problem...Ch. 4 - 5. Find the maximum and minimum values of (if...Ch. 4 - 6. Use graphical methods to minimize subject to ,...Ch. 4 - 7. Express the following linear programming...Ch. 4 - 8. The final simplex matrix for a problem is as...Ch. 4 - 9. Use the simplex method to maximize . Ch. 4 - 10. Use graphical methods to maximize subject...Ch. 4 - 11. Maximize subject to Ch. 4 - 12. River Brewery is a microbrewery that produces...Ch. 4 - 13. A marketing research group conducting a...Ch. 4 - 14. Lawn Rich, Inc., makes four different lawn...

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