Question

an objective function and a system of linear inequalities representing constraints are given. complete parts (a) through (c). objective function z = 4x - 3y constraints 0 ≤ x ≤ 7 0 ≤ y ≤ 9 x + y ≥ 6 a. graph the system of inequalities representing the constraints. use the graphing tool to graph the system. click to enlarge graph

Explanation:

Step1: Rewrite inequalities as equations

Rewrite $x + y\geq6$ as $y\geq - x + 6$, $0\leq y\leq9$ as $y = 0$ and $y = 9$, $0\leq x\leq7$ as $x = 0$ and $x = 7$.

Step2: Graph $y=-x + 6$

Find two points on the line $y=-x + 6$. When $x = 0$, $y=6$; when $y = 0$, $x = 6$. Draw the line $y=-x + 6$ and shade the region above it (since $y\geq - x + 6$).

Step3: Graph $y = 0$ and $y = 9$

Draw two horizontal lines $y = 0$ and $y = 9$. Shade the region between them.

Step4: Graph $x = 0$ and $x = 7$

Draw two vertical lines $x = 0$ and $x = 7$. Shade the region between them.

Step5: Find the intersection region

The intersection of all the shaded - regions is the solution set of the system of inequalities.

Answer:

The graph should show the intersection of the regions defined by $y\geq - x + 6$, $0\leq y\leq9$, and $0\leq x\leq7$. The feasible region is a polygon formed by the intersection of these areas.