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Graphs and Functions

Objective functions with constraints

An objective function is to be maximized given the following constraints: x+2y=4, x-y=1, x=0, y=0. Find the vertices of the set of feasible solutions.

Question about One-to-one functions

Define F: power P({a, b, c}) -> Z as follows: for all A exist in power P({a, b, c}), F(A) = the number of elements in A. a). Is F one-to-one? Please give proof or give a counterexample. Please explain so I may understand. Thanks

Maximal, greatest, minimal, least elements

Given S = {0, 1}, let R be the partial order relation on S X S X S such that for all ordered triples (a, b, c) and (d, e, f) in SXSXS (a, b, c) is related to (d, e, f) &#61659; a =<d, b=<e, c=<f, where =< denotes the usual "less than or equal to" relation for real numbers. Give all maximal, greatest, minimal and least elements

Equation of a line

How do you fine the equation of a line? ~Find the equation of each line described below. Show all subproblems. a) The line through points (-1,4) and (2, 1) b) The line through points (6,3) and (5,5) c) The line with slope 1/3 through the point (0,5) d) The line parallel to y= 2x-5 through point (1,7)