Linear Programming

We are given a linear programming problem (LPP) with the objective function , and the feasible region defined by the constraints and .

Step 1: Find the points of intersection of the lines.

The equations of the lines are:

We solve these two equations to find the points of intersection.

Solve for :

$ x + 3y = 9 y = 2 x + y = 5 (3, 2) Z (0, 5) (5, 0) (3, 2) Z = 11x + 7y (0, 5) (5, 0) (3, 2) Z (5, 0) Z = 55 $.

The formula for the perpendicular distance from a point to the plane is:

In this case, the position vector of the point is given as , and the plane is defined by the vector equation .

Comparing the equation of the plane to the general form , we have:

Substituting the values into the distance formula, we get:

Therefore, the correct option is (1) .