Question

the equality lines for the following constraints are shown in the graph below:
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$$\begin{cases} x \\ge 2 \\\\ y \\ge 2 \\\\ x + y \\ge 7 \\end{cases}$$

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the feasible region is the area represented by the letter

a b c d e f g

Explanation:

Step1: Analyze the first constraint

The constraint \(x \ge 2\) represents the region to the right of the vertical line \(x = 2\).

Step2: Analyze the second constraint

The constraint \(y \ge 2\) represents the region above the horizontal line \(y = 2\).

Step3: Analyze the third constraint

The constraint \(x + y \ge 7\) represents the region above and to the right of the line \(x + y = 7\).

Step4: Identify the overlapping region

The region satisfying all three inequalities is represented by the letter A.

Answer:

A