Advertisements
Advertisements
Question
Solve graphically : 2x + y ≥ 5 and x – y ≤ 1
Solution
First we draw the lines AB and CD whose equations are 2x + y = 5 and x – y = 1 respectively.
| Line | Equation | Points on the X-axis | Points on the Y-axis | Sign | Region |
| AB | 2x + y = 5 | A(2.5, 0) | B(0, 5) | ≥ | non-origin side of line AB |
| CD | x – y = 1 | C(1, 0) | D(0, –1) | ≤ | origin side of line CD |
The solution set of the given system of inequations is shaded in the graph.
APPEARS IN
RELATED QUESTIONS
Solve graphically : y ≥ 0
Solve graphically : x ≤ 0
Solve graphically : y ≤ 0
Solve graphically : x ≥ 0 and y ≥ 0
Solve graphically: x ≤ 0 and y ≥ 0
Solve graphically: 2x – 3 ≥ 0
Solve graphically : 3x + 4 ≤ 0
Solve graphically : 5y + 3 ≤ 0
Solve graphically : x +2y ≤ 6
Solve graphically : 5x – 3y ≤ 0
Solve graphically : x + y ≥ 6 and x + 2y ≤ 10
The corner points of the feasible solutions are (0, 0) (3, 0) (2, 1) (0, 7/3) the maximum value of Z = 4x + 5y is
The half plane represented by 4x + 3y >14 contains the point
If a corner point of the feasible solutions are (0, 10) (2, 2) (4, 0) (3, 2) then the point of minimum Z = 3x + 2y is
A solution set of the inequality x ≥ 0
Check the ordered points (1, −1), (2, −1) is a solution of 2x + 3y − 6 ≤ 0
If the point (x1, y1) satisfies px - qy < 13, then the solution set represented by the inequation is ______
Solution of the LPP minimize z = 7x + 2y subject to x + y ≥ 60, x - 2y ≥ 0, x + 2y ≤ 120, x, y ≥ 0 is ______
The shaded region is represented by the in equations ______
The maximum value of z = 7x + 6y.
Subject to the constraints x ≤ 45, y ≤ 55 and x ≥ 0, y ≥ 0 is ______.
Region represented by the inequalities x ≥ 0, y ≤ 0 is ______.
If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x4 + 12x3 - 36x2 + 25, x ∈ R, then ______
Determine the system of linear equation for which the solution set is the shaded region in the following figure ______.
Solution set of the inequality y ≥ 0 is ______.
The set of real x satisfying the inequality `(5 - 2x)/3 ≤ x/6 - 5` is [a, ∞). The value of ‘a’ is ______.
Which of the following linear inequalities satisfy the shaded region of the given figure?
The object function z = 4x1 + 5x2, subject to 2x1 + x2 ≥ 7, 2x1 + 3x2 ≤ 15, x2 ≤ 3, x1, x2 ≥ 0 has minimum value at the point is ______.
The objective function of LPP defined over the convex set attains it optimum value at ______.
