Question

an objective function and a system of linear inequalities representing constraints are given. complete parts (a) through (c).
objective function $z = 2x-3y$
constraints $\begin{cases}0leq xleq5\\0leq yleq6\\x + ygeq4end{cases}$
a. graph the system of inequalities representing the constraints.
use the graphing tool to graph the system.

Explanation:

Step1: Graph \(0\leq x\leq5\)

Draw vertical lines \(x = 0\) and \(x = 5\), and shade the region between them including the lines.

Step2: Graph \(0\leq y\leq6\)

Draw horizontal lines \(y = 0\) and \(y = 6\), and shade the region between them including the lines.

Step3: Graph \(x + y\geq4\)

Rewrite as \(y\geq -x + 4\). Plot the line \(y=-x + 4\) (with \(y - \)intercept \(4\) and slope \(- 1\)). Shade the region above this line including the line.

Answer:

The feasible - region is the intersection of the shaded regions from the three inequalities. It is a polygon - shaped region bounded by the intersection of the vertical lines \(x = 0\) and \(x = 5\), the horizontal lines \(y = 0\) and \(y = 6\), and the line \(y=-x + 4\).