For a LPP, the objective function is $z=4x+3y$ and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ?

The constraints are -

A. $2x + y \leq 8$

B. $2x + y \geq 8$

C. $x + 2y \leq 10$

D. $x + 2y \geq 10$

E. $x, y \geq 0$

Choose the correct answer from the options given below:

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is:

The corner points of the bounded feasible region of the LPP: Maximize $z = x + y$ subject to constraints $2x + 5y \leq 100$, $8x + 5y \leq 200$, $x \geq 0$, $y \geq 0$ are

The feasible region for a LPP is shown in the figure. The minimum value of Z = 2x - 3y is

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 a two variables linear programming problem (LPP), which of the following statement is correct ?