Questions: What are the coordinates of the corner point where the minimum value of P occurs? Select the correct choice below and fill in any answer boxes present in your choice. A. The coordinates are . (Type an ordered pair.) B. There is no minimum value of P.

Solution Steps

To find the coordinates of the corner point where the minimum value of \( P \) occurs, we need to identify the feasible region defined by the constraints of the problem. Then, we evaluate the objective function \( P \) at each corner point of this region. The corner point that gives the smallest value of \( P \) is the solution.

We are given an objective function \( P \) with coefficients \( c = [1, 1] \). This means we want to minimize \( P = x + y \).

The constraints are given by: \[ \begin{align_} x + 2y & \leq 5 \\ 3x + 4y & \leq 6 \end{align_} \] Additionally, the variables \( x \) and \( y \) must be non-negative: \[ x \geq 0, \quad y \geq 0 \]

The feasible region is defined by the intersection of the constraints: \[ \begin{align_} x + 2y & \leq 5 \\ 3x + 4y & \leq 6 \\ x & \geq 0 \\ y & \geq 0 \end{align_} \]

To find the minimum value of \( P \), we evaluate \( P = x + y \) at each corner point of the feasible region. The corner points are determined by the intersection of the constraints.

Using the given constraints and bounds, the corner point where the minimum value of \( P \) occurs is found to be at \( (0, 0) \).

Final Answer