Explanation Given: The function f ( x , y ) = 4 y − 3 x subject to 2 x + 5 y = 3 . Result used: Theorem 1: Any local maxima or minima of the function z = f ( x , y ) subject to the constraint g ( x , y ) = 0 will be among those points ( x 0 , y 0 ) for which ( x 0 , y 0 , λ 0 ) is a solution of the system F x ( x , y , z ) = 0 F y ( x , y , z ) = 0 F z ( x , y , z ) = 0 Where F ( x , y , λ ) = f ( x , y ) + λ g ( x , y ) , provided that all the partial derivatives exist. Calculation: Rewrite the constraint in the form g ( x , y ) = 0 . 2 x + 5 y = 3 2 x + 5 y − 3 = 0 The function f ( x , y ) = 4 y − 3 x subject to the constraint 2 x + 5 y − 3 = 0 . The form of the function should be F ( x , y , λ ) = f ( x , y ) + λ g ( x , y ) . Substitute f ( x , y ) = 4 y − 3 x and g ( x , y ) = 2 x + 5 y − 3 in F ( x , y , λ ) = f ( x , y ) + λ g ( x , y ) , F ( x , y , λ ) = 4 y − 3 x + λ ( 2 x + 5 y − 3 ) = 4 y − 3 x + λ 2 x + 5 λ y − 3 λ Thus, the function F ( x , y , λ ) = 4 y − 3 x + λ 2 x + 5 λ y − 3 λ

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

See similar textbooks

Videos

Question

Chapter 14.4, Problem 11E

To determine

To explain: The reason for why no maxima or minima exist for the given constraint.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 10E

Chapter 14.4, Problem 12E

Students have asked these similar questions

29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.

4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.

3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.

Chapter 14 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Prob. 5MP Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.