Mathematics : Linear Programming

The constraints - x₁ + x₂ $\le$ 1, - x₁ + 3x₂ $\le$ 9, x₁, x₂ > 0 defines on

• bounded feasible space

• unbounded feasible space

• both bounded and unbounded feasible space

• None of the above

The objective function Z = x₁ + x₂, subject to the constraints are  x₁ + x₂ $\le$ 10, - 2x₁ + 3x₂ $\le$ 15, x₁ $\le$ 6, x₁x₂ $\ge$ 0 has maximum value of _ the feasible region.

• at only one point

• at only two points

• at every point of the segment joining two points

• at every point of the line joining two points equivalent to

The objective function z = 4x₁ + 5x₂, subject to 2x₁ + x₂ $\ge$ 7, 2x₁ + 3x₂ $\le$ 15, x₂ $\le$ 3, x₁x₂ $\ge$ 0 has minimum value at the point

• on X-axis

• on Y-axis

• at the origin

• on the line parallel to X-axis

The objective function of LPP defined over the convex set attains it optimum value at

• atleast two of the corner points

• all the corner points

• atleast one of the corner points

• None of the corner points

If x + y $\le 2, \mathrm{x} \ge 0, \mathrm{y} \ge 0$ the point at which maximum value of 3x + 2y attained will be

• (0, 2)

• (0, 0)

• (2, 0)

• $\left(\frac{1}{2}, \frac{1}{2}\right)$

If an LPP admits optimal solution at two consecutive vertices of a feasible region, then

• the LPP under consideration is not solvable

• the LPP under consideration must be reconstructed

• the required optimal solution is at the mid-point of the line joining two points

• the optimal solution occurs at every point on the line joining these two points

By graphical method, the solution of linear programming problem maxirmze z = 3x₁ + 5x₂ subject to 3x₁ + 2x₂ $\le 18, {\mathrm{x}}_1 \le 4, {\mathrm{x}}_2 \le 6, {\mathrm{x}}_1 \ge 0, {\mathrm{x}}_2 \ge 0$

• x₁ = 2, x₂ = 0, z = 6

• x₁ = 2, x₂ = 6, z = 36

• x₁ = 4, x₂ = 3, z = 36

• x₁ = 4, x₂ = 6, z = 42

If x and y are independent vanables, then the angle between lines of regression is

• 45°

• 0°

• 30°

• 90°

In a linear programming problem z = 2x + y when 5x + 10y $\le$ 50, x + y $\ge$ 1, y $\le$ 4 and x, y $\ge$ 0 minimum value of z is

• 0

• 1

• 2

• 1/2

The maximum value of z = 4x + 2y subject to the constraints 2x + 3y $\le$ 18, x + y $\ge$ 10, x, y $\ge$ 0

• 36

• 40

• 20

• None of these