Question

an objective function and a system of linear inequalities representing constraints are given. complete parts (a) through (c). objective function z = 3x - 2y constraints (\begin{cases}2leq xleq5\ygeq3\\x - ygeq - 4end{cases}) a. graph the system of inequalities representing the constraints. use the graphing tool to graph the system.

Explanation:

Step1: Graph \(2\leq x\leq5\)

The vertical lines \(x = 2\) and \(x = 5\) are solid (since the inequalities are inclusive), and the region between them is shaded.

Step2: Graph \(y\geq3\)

The horizontal line \(y = 3\) is solid, and the region above it is shaded.

Step3: Rewrite and graph \(x - y\geq - 4\)

Rewrite as \(y\leq x + 4\). The line \(y=x + 4\) is solid, and the region below it is shaded.

Answer:

The solution - region is the intersection of the regions obtained from the three inequalities. It is a polygon formed by the intersection of the shaded regions of \(2\leq x\leq5\), \(y\geq3\) and \(y\leq x + 4\). You would use a graphing utility (like a graphing calculator or online graphing tool such as Desmos) to accurately draw the lines \(x = 2\), \(x = 5\), \(y = 3\) and \(y=x + 4\) and shade the appropriate regions.