Linear Inequalities

The linear relationship between two variables in an inequality:

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:

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

XYZ Company has a policy for its recruitment as it should not recruit more than eight men $\displaystyle (x)$ to three women $\displaystyle (y)$. How can this fact be expressed in inequality?

The region indicated by the shading in the graph is expressed by the inequalities

If $\displaystyle 2x + 5 > 3x + 2$ and $\displaystyle 2x - 3 \le 4x - 5$, the '$\displaystyle x$' can take which of the following value?

In a garment factory, an average experienced tailor can stitch $\displaystyle 5$ shirts while a fresh tailor can stitch $\displaystyle 3$ shirts daily, but the employer has to maintain an output of at least $\displaystyle 30$ shirts stitched per day. This can be formulated as

A fertilizer company produces two types of fertilizers called grade I and grade II. Each of these types is processed through a critical chemical plant unit. The plant has maximum of $\displaystyle 180$ hours availability in a week. Manufacturing one bag of grade I fertilizer requires $\displaystyle 4$ hours in the plant. Manufacturing one bag of grade II fertilizer requires $\displaystyle 10$ hours in the plant. Express this using linear inequalities.

The solution of the inequality $\displaystyle \frac{5 - 2x}{3} \le \frac{x}{6} - 5$

A software company should recruit more than or equal to $\displaystyle 10$ employees at a time for their recruitment drive. Under these conditions, company recruits experienced $\displaystyle (x)$ and freshers $\displaystyle (y)$ employees. The values of $\displaystyle x$ and $\displaystyle y$ can be related by the following inequality

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?

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

The common region represented by the following in equalities $\displaystyle L_1: x + y \le 4; L_2: 2x + y \ge 2$ is

Given the constraints, $\displaystyle x \le 3, y \le 4$ and $\displaystyle 4x + 3y \le 12$, the point ______ is in the feasible region. (Select from the below given list)

A senior typist can type five reports and a junior typist can type three reports per day. But the management needs to complete at least $\displaystyle 30$ reports in a day. If $\displaystyle S$ and $\displaystyle J$ denote the number of senior and junior typists assigned for the work. Which of the following inequality represents the constraint?

The shaded area is represented by which of the following option?

A manufacturer produces two items A and B. He has $\displaystyle \text{₹}10,000$ to invest and a space to store $\displaystyle 100$ items. A table costs him $\displaystyle \text{₹}400$ and a chair $\displaystyle \text{₹}100$. Express this in the form of linear inequalities.

The Solution of the in equality $\displaystyle 8x+6 < 12x+14$ is

The rules and representations demand that employed should employ not more than $\displaystyle 8$ experienced leads to $\displaystyle 1$ fresh one and then fact can be expressed as

On the avg. experienced person does $\displaystyle 6$ units work while A person $\displaystyle 2$ units of work daily but employer has to maintain as output of at least $\displaystyle 24$ units of per day. This situation can be expressed as

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

A company produces two products A and B, each of which requires processing in two machines. The first machine can be used for most for $\displaystyle 60$ hours, the second machine can be used for most for $\displaystyle 40$ hours. The product A requires $\displaystyle 2$ hours on machine one and one hour on machine two. The product B requires one hour on machine one and two hours on machine two. Express above situation using linear inequalities

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

On the average experienced person does $\displaystyle 5$ units of work while a fresh one $\displaystyle 3$ units of work daily but the employer has to maintain an output of at least $\displaystyle 30$ units of work per day. This situation can be expressed as

The sol. set of the eq. $\displaystyle x+2 > 0$ and $\displaystyle 2x-6 > 0$ is

The solution space of the inequalities $\displaystyle 2x+y \le 10$ and $\displaystyle x-y \le 5$: (i) includes origin (ii) includes the point $\displaystyle (4, 3)$ Which one is correct?

The sol. of the inequality $\displaystyle \frac{(5-2x)}{3} < \frac{x}{6}-5$ is

On the average, experienced person does $\displaystyle 5$ units of work while a fresh one $\displaystyle 3$ units work daily but the employer have to maintain the output of at least $\displaystyle 30$ units of work per day. This situation can be expressed as.

Solution space of the inequalities $\displaystyle 2x+y \le 10$ and $\displaystyle x-y \le 5$: (i) Includes the origin (ii) Includes the point $\displaystyle (4, 3)$ Which one is correct?

What is the smallest integral value of $\displaystyle n$ for which $\displaystyle n^2+7n-50n-336 > 0$

On the average experienced person does $\displaystyle 5$ units of work while a fresh one $\displaystyle 3$ units of work daily, but the employer have to maintain the output at least $\displaystyle 30$ units of work per day. The situation can be expressed as

A dealer has only $\displaystyle \text{₹} 5760$ to invest in fans (x) and sewing machines (y). The cost per unit of fan and sewing machine is $\displaystyle \text{₹} 360$ and $\displaystyle \text{₹} 240$ respectively. This can be shown by:

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

The rules and regulations demand that the employer should employ not more than $\displaystyle 5$ experienced hands to $\displaystyle 1$ fresh one and this fact is represented by (Taking experienced person as $\displaystyle x$ and fresh person as $\displaystyle y$)

The common region represented by the following in equalities $\displaystyle L_1 = X_1 + X_2 \le 4$; $\displaystyle L_2 = 2X_1 + X_2 \ge 6$

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

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

A Labour can be paid under two methods given below: (i) $\displaystyle `600`$ fixed and $\displaystyle `50`$ per hour (ii) $\displaystyle `170`$ per hour If a labour job work takes '$\displaystyle r$' hours to complete, find out the value of '$\displaystyle r$' for which the method (ii) gives the labour gets the better wages.

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

If $\displaystyle 3x + 2 < 2x + 5$ and $\displaystyle 4x - 5 \ge 2x - 3$, then x can take from the following values

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

If $\displaystyle 2x + 5 < 3x + 2$ and $\displaystyle 2x - 3 \ge 4x - 5$ then x takes which of the following value?

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

On an average an experienced person does 5 units of work whereas an unexperienced does one 3 units work daily but the employer have to maintain the output of at least 30 units of work per day. The situation can be expressed as.

Graph of the following linear inequalities : $\displaystyle x+y \ge 1, y \le 5, x \le 6, 7x+9y \le 63, x \ge 0, y \ge 0$ is given below:Mark the common region.

A manufacturer produces two items A and B. He has $\displaystyle `10,000`$ to invest and a space to store $\displaystyle `100`$ its ms. A table costs $\displaystyle `100`$ and a chair $\displaystyle `40`$. Express this in the form of linear inequalities.

If $\displaystyle 2x + 5 < 3x + 2$ and $\displaystyle 2x - 3 \ge 4x - 5$, then x takes which of the following value ?

Solve Inequalities $\displaystyle 2 \le \frac{3x - 2}{5} \le 4$ where $\displaystyle x \in N$

The shaded region represents:

The solution of the inequality $\displaystyle 1 \le \frac{(5 - 2x)}{3} \le 5$

A manufacturer produces two products A and B. The profit on product A is ₹ 8 on each unit and profit on product B is ₹ 13 on each unit. Then the objective function is

A company produce two type of product A & B which require processing in two machines. First machine can be used up to 15 hrs. and second can be used at most 12 hrs. in a day. The product A requires 2 hrs. on machine 1 & 3 hrs. on machine 2. The product B requires 3 hrs. on machine 1 & 1 hour on machine 2. This can be expressed as :

The time required to produce a unit of product A is 3 hours and that for product B is 5 hours. The total usable time is 220 hours. If x and y are the no. of units of A and B that are produced then

Mr. A plans to invest up to $\displaystyle \text{₹} 30,000$ in two stocks X and Y. Stock X(x) is priced at $\displaystyle \text{₹} 175$ and Stock Y(y) at $\displaystyle \text{₹} 95$ / share. This can be shown by

A small manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry then sent to the machine shop for finishing. The number of man-hours of labour required in each shop for the production of each unit of A and B, and the number of man-hours the firm has available per week are as follows:GadgetFoundryMachine-shopA105B64Weekly capacity1000600Let the firm manufactures x units of A and y units of B. The constraints are:

On solving the inequalities $\displaystyle 2x+5y \le 20, 3x+2y \le 12, x \ge 0, y \ge 0$, we get the following situation

The solution of the inequality $\displaystyle \frac{5-2x}{3} \le \frac{x}{6} - 5$ is

Solve the system and $\displaystyle \frac{5-2x}{4} \le \frac{x}{8} - 5$ and $\displaystyle \frac{x+4}{3} \le 6$.

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 common region represented by inequalities: $\displaystyle 2x + y \ge 8, x + y \ge 12, 3x + 2y \le 34, x \ge 0$ and $\displaystyle y \ge 0$ is

On solving the inequalities $\displaystyle 6x + y \ge 18$, $\displaystyle x + 4y \ge 12$, $\displaystyle 2x + y \ge 10$; which of the following are correct solutions?

The longest side of a triangle is 2 times the shortest side and the third side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

Which of the following is a solution of the inequality $\displaystyle \frac{5x}{3} \le \frac{x}{6} - 5$ ?

The number of solutions of $\displaystyle \frac{5-2x}{4} \le \frac{x}{8} - 5 > 3-2x$ are ___________, where $\displaystyle x$ is a real number.

The region specified by the inequalities $\displaystyle 10x+29y \ge 40$ and $\displaystyle 15x-4y \le 25$ includes the point