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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Chapter 4, Problem 8T
To determine
The solutions of the dual maximization problem and the minimization problem, label each solution.
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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
To
Hamilton Butler
Clermont
Southern Gas
10
20
15
Northwest Gas
12
15
18
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
Assignment 3 graph.docx
Score: 1 out of 1
Comment:
(b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs (in thousands of…
Use the method of undetermined coefficients to solve the given nonhomogeneous system.
dx
dt
=
2x + 3y − 8
dy
dt
=
−x − 2y + 6
X(t) =
As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk.
(a)
Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%.
Assume
that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let
ds ≥ R − Rs
with
ds ≥ 0.
Then make the objective function:
Min
1
5
5
s = 1
ds2.
Let
FS = proportion of portfolio invested in the foreign stock mutual fund
IB = proportion of portfolio invested in the intermediate-term bond fund
LG = proportion of portfolio invested in the large-cap growth fund
LV = proportion of portfolio invested in the large-cap value fund…
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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