Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 22, Problem 12P
Develop a user-friendly computer program for adaptive quadrature based on Fig. 22.5. Test it by solving Prob. 22.10.
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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.)
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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
=
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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 22 Solutions
Numerical Methods for Engineers
Ch. 22 - 22.1 Use order of Romberg integration to...Ch. 22 - Use Romberg integration to evaluate I=12(x+1x)2dx...Ch. 22 - Use Romberg integration to evaluate 02exsinx1+x2dx...Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - 22.6 Obtain an estimate of the integral from Prob....Ch. 22 - 22.7 Perform the computation in Examples 21.3 and...Ch. 22 - Employ two- through six-point Gauss-Legendre...Ch. 22 - Prob. 9PCh. 22 - 22.10 Develop a user-friendly computer program for...
Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - 22.13 Develop a user-friendly computer program for...Ch. 22 - There is no closed form solution for the error...Ch. 22 - 22.15 The amount of mass transported via a pipe...Ch. 22 - The depths of a river H are measured at equally...Ch. 22 - 22.17 Recall that the velocity of the freefalling...Ch. 22 - 22.18 Prove that Eq. (22.15) is equivalent to...
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