Reference no: EM13962696

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