Question

All parts of this problem refer to the following feasible region and objective function. x ≥ 0 x ≥ y x+2 y ≤ 12 x+y ≤ 10 P=x+4 y If we continue to decrease the value of P, at which vertex of the feasible region will these lines first touch the feasible region?

Answer 1

To determine at which vertex of the feasible region the lines first touch the feasible region when decreasing the value of P, we need to solve the system of inequalities and equations and find the intersection points.

Step-by-step explanation:

To determine at which vertex of the feasible region the lines first touch the feasible region when decreasing the value of P, we need to find the point where the lines intersect. We can find the intersection points by solving the system of inequalities and equations.

1. Start with the inequalities:

• x ≥ 0
• x ≥ y
• x + 2y ≤ 12
• x + y ≤ 10

2. Graph these inequalities on a coordinate plane to find the feasible region.

3. Next, we have the objective function: P = x + 4y. Decrease the value of P until it touches the feasible region at a vertex. Identify the coordinates of that vertex.

4. Calculate the value of P at that vertex to determine the minimum value.

By following these steps, you can find the vertex of the feasible region where the lines first touch when decreasing the value of P.