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

18.

The maximum value of $\mathrm{\mu }$ = 3x + 4y, subject to the conditions x + y $\le$ 40, x + 2y $\le$ 60, x, y $\ge$ 0, is

• 130

• 140

• 40

• 120

If x + y $\le$ 2; x $\ge$ 20, y $\ge$ 20, then the point, at which the maximumvalue of 3x + 2y is attained, will be

• (0, 0)

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

• (2, 0)

• (0, 2)

The maximum value of P = 6x + 8y, if 2x + y $\le$ 30, x + 2y $\le$ 24; x $\ge$ 20, y $\ge$ 20, will be

• 90

• 120

• 96

• 240