Question

Enter 3850, not 3,850.

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Consider the following linear programming.

Minimize 2X + Y
Subject to 3X + 2Y >= 12
2X + 2Y >= 7
X + 2Y >= 6
X >= 2
Y >= 1

Draw the plot for the feasible region.

This linear programming has _________ corner points. (Enter the number of corner points)

The objective value for the optimal corner point is _________.

The objective value for the second-best corner point is __________.

Suppose I start decreasing the coefficient of X in the objective function (currently 2). What is the value of the coefficient at which the current second-best corner point becomes an optimal solution? Enter your answer here: _________. (You need to enter the value of the new coefficient, NOT the change NOR the value of objective.)

Answer 1

To solve the linear programming problem, graph the constraints to identify the feasible region's corner points, then apply the objective function to find the optimal solution and necessary coefficients.

Step-by-step explanation:

The linear programming problem provided requires us to minimize 2X + Y given a set of constraints. To solve this, we first graph the constraints to find the feasible region. The constraints 3X + 2Y >= 12, 2X + 2Y >= 7, X + 2Y >= 6, X >= 2, and Y >= 1 form a polygon on the coordinate plane. After plotting these on a graph, we determine the vertices (corner points) of the feasible region.

Once we have the feasible region, we can apply the objective function to each corner point to determine which one will give us the minimum value. By doing this, we identify the optimal solution and find out the number of corner points. Additionally, we can experiment with the coefficient of X in the objective function to see when the second-best solution becomes the optimal one by linearly modifying the coefficient and comparing the objective values at different corner points.