The region represented by the system of inequalities $x, y \geq 0$ ; $2x + 3y \geq 4$ ; $x \geq 1$ is :

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize $z = c_1x_1 + c_2x_2 + ..... + c_nx_n$ is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

Consider the Linear Programming Problem

Maximize $z = x + y$

Subject to the constraints $x - y \leq -1$, $x \geq y$, $x \geq 0, y \geq 0$

Then which one of the following is TRUE?

For the linear programming problem (LPP),

$Maximize Z = 7x + 9y$, subject to constraints,

$x - y \le -1, -x + y \le 0, x, y \ge 0.$

Which of the following is correct?

Ravi rides his motor cycle at 25 km per hour, he has to spend ₹ 4 per kilometer on petrol, if he rides at a faster speed of 40 km per hour, the petrol cost increases to ₹ 10 per kilometer. He can spend ₹ 200 on petrol and wishes to maximize distance he can travel within one hour. Which of the following is/are TRUE?

A. Maximum distance covered in one hour is 30 km

B. The distance covered at speed of 25km/hr is 50/3 km

C. The distance covered at speed of 25km/hr is $\frac{25}{2}$ km

D. The distance covered at speed of 40km/hr is $\frac{75}{4}$ km

Choose the correct answer from the options given below:

Consider the linear programming problem(LPP):

Minimize $Z = x + y$

$x + 2y \leq 4,$

$3x + y \geq 3,$

$4x + 3y \geq 6,$

$x, y \geq 0.$

Which of the following is correct for the above linear programming problem (LPP):

(A) The LPP has a bounded feasible region.

(B) The LPP has a unique optimal solution.

(C) The optimal value of the LPP exists at the point (3/2, 0)

(D) The corner points of the feasible region are (3/2, 0), (3/5, 6/5), (2/5, 6/5) and (4, 0)

Choose the correct answer from the options given below:

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