Objective function $Z = 200x + 500y$, subject to constraint, $x + 2y \geq 10, 3x + 4y \leq 24$, $x \geq 0, y \geq 0$ - (iii), the minimum value of Z is :

If objective function $Z = 20x + 30y$ of an LPP is subject to the constraints $3x + 4y \geq 12$, $4x + y \geq 4$, $x \geq 0, y \geq 0$, then Z has :

(A) Min at (0, 4)

(B) Max at (0, 4)

(C) Min at (4, 0)

(D) Max at (4, 0)

(E) Min at $\left(\frac{4}{13}, \frac{36}{13}\right)$

Choose the correct answer from the options given below :

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

The feasible reason for the constraints $x \geq 0$, $x + y \leq 1$ and $x - y \leq 1$, is situated in :

(A) I and II quadrant only

(B) I Quadrant

(C) II and IV Quadrant

(D) IV Quadrant

(E) I , II , III and IV Quadrant

Choose the correct answer from the option given below :

A company produces two types of belts A & B with a profit of Rs 2 and Rs 1.50 respectively. Belt of type A needs twice as much time to make as belt type B . The company can produce at the most 1000 belts of type B per day . Material for 800 belts is available per day . At the most , 400 buckles for belt type A and 700 for belts type B are available . Then the appropriate LPP is :

For the LPP, Min $Z = 6x + 10y$ subject to $x \geq 6, y \geq 3, 2x + y \geq 10, x \geq 0, y \geq 0$, redundant constraint is :

The objective function $z = 4x + 3y$ can be maximised subject to the constraints $3x + 4y \leq 24$, $8x + 6y \leq 48$, $x \leq 5$, $y \leq 6$, $x \geq 0$, $y \geq 0$ :