Question

an objective function and a system of linear inequalities representing constraints are given. complete parts (a) through (c). objective function z = 2x - 4y constraints {0≤x≤7, 0≤y≤8, x + y≥6} a. graph the system of inequalities representing the constraints. use the graphing tool to graph the system.

Explanation:

Step1: Graph \(0\leq x\leq7\)

The vertical lines \(x = 0\) and \(x=7\) and the region between them (including the lines) are considered.

Step2: Graph \(0\leq y\leq8\)

The horizontal lines \(y = 0\) and \(y = 8\) and the region between them (including the lines) are considered.

Step3: Graph \(x + y\geq6\)

Rewrite as \(y\geq - x+6\). Plot the line \(y=-x + 6\) (with \(y - intercept = 6\) and slope=-1) and shade the region above the line (including the line).

Answer:

The feasible - region is the intersection of the regions defined by the three inequalities \(0\leq x\leq7\), \(0\leq y\leq8\) and \(x + y\geq6\). It is a polygon bounded by the intersection of the lines \(x = 0\), \(x = 7\), \(y = 0\), \(y = 8\) and \(y=-x + 6\).