Which constraints correctly represent the situation 'mixture of x and y must be at least 8 units' ?

The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

The Solution set of the inequality three $3x + 4y \leq 12$ is :

Given a linear programming problem,

Max $Z = 22x + 18y$, Subject to constraints

$x + y \leq 20, 360x + 240y \leq 5760, x \geq 0, y \geq 0$. Its corner points are :

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 :

Match List - I with List - II.

Choose the correct answer from the options given below :

A carpenter earns a profit of ₹ 50 and ₹ 80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as :

The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively :