Explore BrainMass

Explore BrainMass

    Vector Space Axioms, Zero Element and Geometric Method of Linear Programming

    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!

    Please see the attached file for the fully formatted problems.

    1) Let R+={x/0<x} (that is, the set of positive real numbers). Define the operation of addition on this set by x+y=xy. Show that with this definition there is a zero element, and that every x in R+ has an inverse. Determine what the zero element is, and for any given x, what its additive inverse is.

    2) Let V= {(x,y)/y=x+2} with addition and multiplication by a scalar defined on V by:
    (x,y) + (u,v)= (x+u,y+v-2)
    k (x,y)= (kx,k (y-2) +2)
    Check to see if the vector space axioms 4 (existence of a 0 vector) and 5 (existence of an inverse) are satisfied. If they are, show the 0 vector and the inverse, and if they are not, show why not.

    3)Use the geometric method of linear programming to maximize the objective function f(x,y)=4x-3y subject to the following constraints.
    x is greater than or equal to 0
    x+2y is greater than or equal to 4
    x+y is less than or equal to 6
    2x-2y is less than or equal to 8
    3x-y is less than or equal to 2

    © BrainMass Inc. brainmass.com November 30, 2021, 2:08 am ad1c9bdddf
    https://brainmass.com/math/linear-programming/vector-space-axioms-zero-element-and-geometric-method-of-linear-programming-154753

    Attachments

    Solution Summary

    Vector Space Axioms, Zero Element and Geometric Method of Linear Programming are investigated. The solution is detailed and well presented.

    $2.49

    ADVERTISEMENT