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

The feasible region for a linear programming problem is shown in the figure.

Let $Z = 3x - 4y$ be the objective function, then minimum of Z occurs at the point

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:

An objective function $Z=a x+b y$ is maximum at points $(8,2)$ and $(4,6)$. If $a \geq 0$ and $b \geq 0$ and $a b=25$, then the maximum value of the function is equal to :

Consider the LPP: Maximize $z = x + y$ subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x,y \geq 0$. The optimal feasible solution is

Refer to the LPP given by $Z = 2.5x + y$, subject to constraints

$3x + y \le 12; 3y + x \le 12; x, y \ge 0$:

In the given figure, If $Z_A$ = value of Z at A, $Z_C$ = value of Z at C and Max.(Z) = maximum value of Z, then which of the following relations between $Z_A$, $Z_C$ and Max.(Z) are correct?

A. $2Z_A = 5$ Max.(Z)

B. $5Z_A = 2Z_C$

C. $Z_A = 6 + Z_C$

D. $6+Z_A = Z_C$

Choose the correct answer from the options given below:

The maximum value of $z = 4x + 3y$, if the feasible region for an LPP is as shown below is: