Nonlinear Optimization

The purpose of this assignment is to introduce how to find solutionsto business problems using nonlinear optimization techniques.Using specified data files, chapter example files, and templatesfrom the “Topic 7 Student Data, Template, and ExampleFiles” topic material, complete Chapter 14, Problems 69, 70(ignore the SolverTable portion), 72 (ignore the SolverTable portion),and 94. Use Microsoft Excel’s Solver Add-In to complete theseproblems. For Problems 70, 72, and 94, run the Solver’s Answerand Sensitivity Reports. Interpret and summarize the key results.

To receive full credit on the assignment, complete the following.

Ensure that all Solver settings are defined through the use ofthe Solver dialog box.Ensure that Excel files include theassociated cell functions and/or formulas if functions and/orformulas are used.Include a written response to allnarrative questions presented in the problem by placing it in theassociated Excel file.Include Answer and SensitivityReports interpretation and summary of key results.Placeeach problem in its own Excel file. Ensure that your first and lastname are in your Excel file names.

APA style is not required, but solid academic writing is expected.

This assignment uses a rubric. Please review the rubric prior tobeginning the assignment to become familiar with the expectations forsuccessful completion. QUESTION 1- Can linear and nonlinear optimization problems use the same approach tofind a solution? For example, if the GRG algorithm is used to solve anonlinear optimization problem, will it work to solve a linearoptimization problem? Discuss whether or not the GRG algorithm willalways find a corner point similar to the feasible-region approach. QUESTION 2- Nonlinear optimization problems can have multiple solutions, and asolution can be local or global. Can there be multiple local solutions?Explain your answer. Can there be multiple global solutions? Explain ouranswer. that yields an expected annual return of at least 0.14.
94. You have $50,000 to invest in three stocks. Let R, be
the random variable representing the annual return
on $1 invested in stock i. For example, if R; 0.12,
then $1 invested in stock i at the beginning of a year
is worth $1.12 at the end of the year. The means are
E(R,) = 0.14, E(R2) = 0.11, and E(R3) = 0.10. The
variances are Var R1 = 0.20, Var R2 = 0.08,
and Var R3 = 0.18. The correlations are r 12 = 0.8,
r 13 = 0.7, and r23 = 0.9. Determine the minimum-
variance portfolio that attains an expected annual
return of at least 0.12.
Level B.
Level A
70. In the electricity pricing model, we assumed that the
capacity level is a decision variable. Assume now that
capacity has already been set at 0.65 million of mWh.
(Note that the cost of capacity is now a sunk cost, so it
is irrelevant to the decision problem.) Change the model
appropriately and run Solver. Then use SolverTable to
see how sensitive the optimal solution is to the capacity
level, letting it vary over some relevant range. Does it
appear that the optimal prices will be set so that demand
is always equal to capacity for at least one of the two
periods of the day?
69. In the electricity pricing model, the demand functions
have positive and negative coefficients of prices. The
negative coefficients indicate that as the price of a
product increases, demand for that product decreases.
The positive coefficients indicate that as the price of
a product increases, demand for the other product
increases.
a. Increase the magnitudes of the negative coefficients
from -0.013 and -0.015 to -0.018 and -0.023,
and rerun Solver. Are the changes in the optimal
solution intuitive? Explain.
b. Increase the magnitudes of the positive coefficients
from 0.005 and 0.003 to 0.007 and 0.005, and rerun
Solver. Are the changes in the optimal solution
intuitive? Explain.
c. Make the changes in parts a and b simultaneously
and rerun Solver. What happens now?
71. For each of the following, answer whether it makes
sense to multiply the matrices of the given sizes. In
each case where it makes sense, demonstrate an exam-
ple in Excel, where you make up the numbers.
a. AB, where A is 3 x 4 and B is 4 x 1
b. AB, where A is 1 x 4 and B is 4 x 1
c. AB, where A is 4 x 1 and B is 1 x 4
d. AB, where A is 1 x 4 and B is 1 x 4
e. ABC, where A is 1 x 4, B is 4 x 4, and C is 4 x 1
748 Chapter 14 Optimization Models
9780357233344, Business Analytics: Data Analysis & Decision Making, Sixth Edition, S. Christian Albright – © Cengage Learning.
All Rights Reserved. No distribution allowed without express authorization. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-247. Distributed by Grand Canyon University.
72. Add a new stock, stock 4, to the portfolio optimiza-
tion model. Assume that the estimated mean and
standard deviation of return for stock 4 are 0.125 and
0.175, respectively. Also, assume the correlations
between stock 4 and the original three stocks are 0.3
0.5, and 0.8. Run Solver on the modified model,
where the required expected portfolio return is again
0.12. Is stock 4 in the optimal portfolio? Then run
SolverTable as in the example. Is stock 4 in any of
the optimal portfolios on the efficient frontier?
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