Question

For the constraints given below, which point is in the feasible region of this maximization problem?

(1) 14x + 6y ≤ 42
(2) x - y ≤ 3
(3) x, y ≥ 0__

A. x = 4, y = 4
B. x = 2, y = 8
C. x = 2, y = 1
D. x = 1, y = 5
E. x = -1, y = 1

Answer 1

To find the point in the feasible region, we need to check if each point satisfies all the given constraints. Point C (x = 2, y = 1) is the only point that satisfies all the given constraints.

Step-by-step explanation:

To determine which point is in the feasible region of this maximization problem, we need to check if each point satisfies all the given constraints. Let's check the constraints:

1. For constraint (1): 14x + 6y ≤ 42, substituting the values of each point, we find that points A, C, and D satisfy this constraint.
2. For constraint (2): x - y ≤ 3, substituting the values of each point, we find that points A, B, C, and E satisfy this constraint.
3. For constraint (3): x, y ≥ 0, all points satisfy this constraint.

Combining all three constraints, we see that point C (x = 2, y = 1) is the only point that satisfies all the given constraints. Therefore, the point in the feasible region of this maximization problem is C. Hence, the correct answer is option C: x = 2, y = 1.

Answer 2

C. (x, y) = (2, 1)

Step-by-step explanation:

You want to know which of the offered points is in the feasible region defined by the inequalities ...

• 14x +6y ≤ 42
• x -y ≤ 3
• x ≥ 0
• y ≥ 0

Feasible region

In the attached graph, we have reversed the inequalities so the feasible region is the white area of the graph, together with the dashed boundary lines.

The only point in the feasible region is ...

C. x = 2, y = 1

__

Additional comment

We like to plot multiple inequalities in reverse. That way, the shaded regions show the points excluded from the feasible region.

It can be difficult to discern the feasible region when multiple inequalities overlap, but it shows up nicely when there is no shading in the feasible region at all.

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