Advertisements
Advertisements
प्रश्न
Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0
उत्तर
3x + 2y ≤ 150 … (1)
x + 4y ≤ 80 … (2)
x ≤ 15 … (3)
The graph of the lines, 3x + 2y = 150, x + 4y = 80, and x = 15, are drawn in the figure below.
Inequality (1) represents the region below the line, 3x + 2y = 150 (including the line 3x + 2y = 150). Inequality (2) represents the region below the line, x + 4y = 80 (including the line x + 4y = 80). Inequality (3) represents the region on the left hand side of the line, x = 15 (including the line x = 15).
Since x ≥ 0 and y ≥ 0, every point in the common shaded region in the first quadrant including the points on the respective lines and the axes represents the solution of the given system of linear inequalities.
APPEARS IN
संबंधित प्रश्न
Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0
Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1
Solve the following system of inequalities graphically: x + y ≤ 6, x + y ≥ 4
Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
Solve the following system of inequalities graphically: 5x + 4y ≤ 20, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Solve the following system of inequalities graphically: x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1
Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0
Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.
Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.
A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by\[F = \frac{9}{5}C + 32\]
A solution is to be kept between 30°C and 35°C. What is the range of temperature in degree Fahrenheit?
A company manufactures cassettes and its cost and revenue functions for a week are \[C = 300 + \frac{3}{2}x \text{ and } R = 2x\] respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?
The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
Write the set of values of x satisfying |x − 1| ≤ 3 and |x − 1| ≥ 1.
Write the solution set of the inequation \[\left| \frac{1}{x} - 2 \right| > 4\]
Write the number of integral solutions of \[\frac{x + 2}{x^2 + 1} > \frac{1}{2}\]
Write the solution of set of\[\left| x + \frac{1}{x} \right| > 2\]
Write the solution set of the inequation |x − 1| ≥ |x − 3|.
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400
Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0.
Solution set of x ≥ 0 and y ≤ 0 is
