Explore BrainMass

Explore BrainMass

    Management Science Statements

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Category: Business > Management
    Subject: Management Science
    Details: 1. Which of the following statements are true for f(x) = x2? (Chapter 10)

    a. f(x) is a concave function
    b. f(x) </= 20 is a convex set
    c. f(x) >/= 5 is a convex set
    d. none of the above

    2. Which of the following statements are true for f(x) = 3x2 + 2x + 5? (Chapter 10)

    a. f(x) is not a concave function
    b. f(x) </= 10 is a convex set
    c. f(x) > /= 2 is a convex set
    d. all of the above

    3. Which of the following statements are true for an unconstrained optimization problem? (Chapter 10)

    a. At a global min or max all partial derivatives will be equal to 0.
    b. The first-order optimally conditions are used to find the local maxima and
    local minima.
    c. At a local min or max all partial derivatives will be equal to 1.
    d. none of the above

    4. The Lagrange multiplier _______________. (Chapter 10)

    a. is the shadow price
    b. in not valid over a range of changes in the RHS
    c. is the rate of change in the objective value as the RHS of the constraint
    increases
    d. all the above

    5. The optimal value function of a portfolio analysis problem solved using quadratic
    programming is __________________. (Chapter 10)

    a. called the efficient frontier
    b. hurt when an active constraint is tightened
    c. a piecewise quadratic convex function
    d. all the above

    6. Increasing the RHS on a nonlinear </= constraint __________. (Chapter 10)

    a. can contract the constraint set
    b. may contract the constraint set
    c. may hurt the optimal objective value
    d. none of the above

    © BrainMass Inc. brainmass.com March 4, 2021, 5:57 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/management-science-statements-20231

    Solution Preview

    1. Which of the following statements are true for f(x) = x2? (Chapter 10)
    <br>
    <br>a. f(x) is a concave function
    <br>b. f(x) &lt;/= 20 is a convex set
    <br>c. f(x) &gt;/= 5 is a convex set
    <br>d. none of the above
    <br>Answer b: A set S is called a convex set if the line segment joining any pair of points of S lies entirely in S. Consider 2 points -(20)0.5, (20)0.5. If we square -(20)0.5, (20)0.5 then we get (20,20), both of these are &lt;/= 20 (this matches the requisites for part b). Now, we check if they are convex. Let us arbitrarily take a linear combination of -(20)0.5, (20)0.5 let us say (-(20)0.5+(20)0.5)/2 or 0. Now, let us square 0 and we get 0. Is 0 &lt;/= 20? Yes it is, hence part b) is right.
    <br>2. Which of the following statements are true for f(x) = 3x2 + 2x + 5? (Chapter 10)
    <br>
    <br>a. f(x) is not a concave function
    <br>b. f(x) &lt;/= 10 is a convex set
    <br>c. f(x) &gt; /= 2 is a convex set
    <br>d. all of ...

    $2.49

    ADVERTISEMENT