Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Textbook Question
Chapter 4.1, Problem 12E
In Problems 7-12, the graph of the boundary equations for each system of inequalities is shown with that system. Locate the solution region and find the corners.
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Calculs Insights
πT
| cos x |³ dx
59
2
2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)
Chapter 4 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
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 - Prob. 15ECh. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - In Problems 13-26, graph the solution of each...Ch. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 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 - Prob. 34ECh. 4.1 - Prob. 35ECh. 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 - Prob. 10ECh. 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 - Prob. 14ECh. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - Prob. 16ECh. 4.2 - In Problems 13-24, solve the following linear...Ch. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 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 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 - 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 - Prob. 2CPCh. 4.3 - Prob. 3CPCh. 4.3 - Prob. 4CPCh. 4.3 - Prob. 5CPCh. 4.3 - Prob. 6CPCh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Problems 7-10, a simplex matrix is given in...Ch. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - In Problems 11-18, a simplex matrix for a standard...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - 28. Maximize subject to
Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Problems 31-38 involve linear programming problems...Ch. 4.3 - Problems 31-38 involve linear programming problems...Ch. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - In Problems 35-38, use the simplex method to...Ch. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 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 - Prob. 51ECh. 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 - Prob. 2CPCh. 4.4 - Prob. 3CPCh. 4.4 - Prob. 4CPCh. 4.4 - Prob. 5CPCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - In Problems 5 and 6, suppose a primal minimization...Ch. 4.4 - Prob. 6ECh. 4.4 - In Problems 7-10, write the dual maximization...Ch. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - In Problems 7-10, write the dual maximization...Ch. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - In Problems 17-20, use Excel or some other...Ch. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 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 - Prob. 24ECh. 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 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - In Problems 31-36, use the simplex method, Excel,...Ch. 4.4 - Prob. 33ECh. 4.4 - In Problems 31-36, use the simplex method, Excel,...Ch. 4.5 - Prob. 1CPCh. 4.5 - 2. Using the matrix from Problem 1, find the...Ch. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - In Problems 19-26, use the simplex method or...Ch. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Problems 27-30 involve maximization with mixed...Ch. 4.5 - Prob. 28ECh. 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 - Prob. 33ECh. 4.5 - Prob. 34ECh. 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 - Prob. 38ECh. 4 - In Problems 1-4, use the given feasible region...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - In Problems 5-8, a function and the graph of a...Ch. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - In Problems 5-8, a function and the graph of a...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - Prob. 13RECh. 4 - In Problems 9-15, solve the linear programming...Ch. 4 - Prob. 15RECh. 4 - In Problems 16-19, use the simplex method to solve...Ch. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - In Problems 22-25, form the dual and use the...Ch. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - In Problems 28-35, use the simplex method. Assume...Ch. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 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 - Prob. 39RECh. 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 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 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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