The corner points of the feasible region of the LPP: Minimize $Z = -50x + 20y$ subject to $2x - y \geq -5$, $3x + y \geq 3$, $2x - 3y \leq 12$ and $x, y \geq 0$ are

The corner points of a bounded feasible region are $A(15,0), B(40,0), C(4,18)$ and $D(6,12)$. If the objective function is $z = 20x + 10y$, then the difference in maximum and minimum value of $z$ is

In linear programming, the optimal value of the objective function is attained at the points given by

A manufacturer produces two products, A and B. Both products are processed on two different machines. The available capacity of the first machine is 12 hours and of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹7 profit and that of product B at a profit of ₹4. A LPP to maximise the profit is:

For the linear programming problem:

Minimize $z = 2x - 5y$, subject to the constraints:

$x + 2y \ge 10$;

$3x + 4y \le 24$;

$x,y \ge 0$, then optimal value of $z$ is

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:

The maximum value of $z=5x+3y$ subjected to the constraints $2x+3y \ge 60, 2x+y \le 40; x,y \ge 0$ is: