For the given linear programming problem $z = ax + by; a, b > 0$ subject to the constraints $2x + y \leq 10, x + 3y \leq 15, x, y \geq 0$. If the corner points are (0,0), (5,0), (3,4) and (0,5) and z is maximum at both (3,4) and (0,5), then the relationship between a and b is

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s):

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

If the objective function for an LPP is $Z=4x+5y$ and the corner points for bounded feasible region are (10, 0), (5, 3), (2, 5) and (0, 6), then the minimum value of $Z$ occurs at

In reference to a linear programming problem (LPP), which of the following statements are true?

A. The optimal value of the objective function is attained at the points given by intersections of inequation with the axes only.

B. The objective function of a LPP is a linear function to be optimized.

C. Every LPP admits an optimal solution.

D. The region represented by the inequation system, $x, y\geq0$, $x+2y\leq4, 3x+y\geq3, 4x+3y\geq6$ is bounded in the first quadrant.

Choose the correct answer from the options given below:

If the objective function for an LPP is $Z = 2x + 5y$ and the corner points of the bounded feasible region are (0, 0), (5, 0) , $\left(\dfrac{8}{5},\dfrac{6}{5}\right)$ and (0, 2) then the maximum value of $z$ occurs at

The number of corner points of the feasible region of an LPP determined by the constraints $x - y \geq 0$, $2y \leq x + 2, x \geq 0, y \geq 0$ is