Question

Which graph best represents the feasibility region for the system shown below?

Answer 1

Answer: Correct option is 3rd option.

Step-by-step explanation: Given inequalities

x≥ 0

y≤ 8

y ≥ x and

y ≥ $-\frac{1}{2}x +6$.

Let us graph the lines on the calculators first.

x≥ 0 : First inequality line would be a solid line and we would shade right side of y-axis because we have greater than or equal to symbol.

y≤ 8 : Second inequality line would be a solid line and we would shade down the line because we have less than or equal to symbol.

y ≥ x : Third inequality line would be a solid line and we would shade up of the line because we have greater than or equal to symbol.

y ≥ $-\frac{1}{2}x +6$ : Fourth inequality line would be a solid line and we would shade up of the line because we have greater than or equal to symbol.

From the graph we can see that middle portion is the common feasible region.

Therefore, correct option is 3rd option.

Answer 2

The second graph has the right picture