A dietician re-accommodates mixture of two kinds of food to a person so that mixture contains at least $\displaystyle 15$ units of carbs, $\displaystyle 25$ units of protein, $\displaystyle 15$ units of fat and $\displaystyle 15$ units of fiber. The above contains of nutrients are available in the foods as below: Carbs (Food-1: 20, Food-2: 10); Protein (Food-1: 5, Food-2: 2); Fat (Food-1: 3, Food-2: 4); Fibre (Food-1: 2, Food-2: 5). If '$\displaystyle x$' units of food-1 is mixed with '$\displaystyle y$' units of food-2, how dietician recommendation can be expressed?

On solving the inequalities $\displaystyle 5x + y \le 100$, $\displaystyle x + y \le 60$, $\displaystyle x \ge 0$, $\displaystyle y \ge 0$, we get the following solution:

An employer recruits experienced $\displaystyle (x)$ and fresh workmen $\displaystyle (y)$ for his under the condition that he cannot employ more than $\displaystyle 11$ people $\displaystyle x$ and $\displaystyle y$ can be related by the inequality.

The solution set of the equations $\displaystyle x + 2 > 0$ and $\displaystyle 2x - 6 > 0$ is

On solving the inequalities; we get $\displaystyle 6x + y \ge 18$, $\displaystyle x + 4y \ge 12$, $\displaystyle 2x + y \ge 10$

Solve for $\displaystyle x$ of the inequalities $\displaystyle 2 \le \frac{3x - 2}{5} \le 4$ where $\displaystyle x \in N$

The common region in the graph of the inequalities $\displaystyle x + y \le 4$, $\displaystyle x - y \le 4$, $\displaystyle x \ge 2$ is