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12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

Chapter 4.2, Problem 3E

Textbook Problem

In Problems 1-4, use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).

Expert Solution

To determine

**To calculate:** The maximum and minimum points of the given objective function

**Given Information:**

The provided figure is shown below,

**Calculation:**

Consider the provided objective function,

Now, in order to determine, the maximum and minimum value,

Read the graph,

The maximum points lay above the shaded region and the minimum value lay below the shaded region.

As the region is unbounded and open,

So, the coordinates of feasible region are:

The maximum values are the

The minimum value is

Substitute

Substitute

Mathematical Applications for the Management, Life, and Social Sciences

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Ch. 4.1 - 1. Graph the region determined by the...Ch. 4.1 - 2. Determine the corners of the region.
Ch. 4.1 - In Problems 1-6, graph each inequality.
Ch. 4.1 - In Problems 1-6, graph each inequality.
2.
Ch. 4.1 - In Problems 1-6, graph each inequality.
3.
Ch. 4.1 - In Problems 1-6, graph each inequality.
4.
Ch. 4.1 - In Problems 1-6, graph each inequality.
5.
Ch. 4.1 - In Problems 1-6, graph each inequality.
6.
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 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 - 28. Learning environments An experiment that...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 - 32. Manufacturing The Digital Star Company makes...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 - 26. 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 pricesâ€”land management For Problems 35 and...Ch. 4.2 - Shadow pricesâ€”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 - 45. 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 - 39. Manufacturing Q-RAM Inc. manufactures...Ch. 4.3 - 40. Construction A contractor builds two types of...Ch. 4.3 - 41. Production scheduling At one of its factories,...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 - 22. Manufacturing Nekita Corporation assembles...Ch. 4.4 - 23. Manufacturing The Digital Star Company makes...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 - In Problems 37 and 38, use Excel or some other...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 - 41. 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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