Advertisements
Advertisements
प्रश्न
Solve the following linear programming problems by graphical method.
Maximize Z = 22x1 + 18x2 subject to constraints 960x1 + 640x2 ≤ 15360; x1 + x2 ≤ 20 and x1, x2 ≥ 0.
Advertisements
उत्तर
Given that 960x1 + 640x2 ≤ 15360
Let 960x1 + 640x2 = 15360
3x1 + 2x2 = 48
| x1 | 0 | 16 |
| x2 | 24 | 0 |
Also given that x1 + x2 ≤ 20
Let x1 + x2 = 20
| x1 | 0 | 20 |
| x2 | 20 | 0 |
To get point of intersection
3x1 + 2x2 = 48 …..(1)
x1 + x2 = 20 ……(2)
− 2x1 – 2x2 = – 40 …..(3) ......[Equation (2) × –2]
x1 = 8 .....[Adding equation (1) and (3)]
x1 = 8 substitute in (2),
8 + x2 = 20
x2 = 12
The feasible region satisfying all the given conditions is OABC.
The co-ordinates of the comer points are O(0, 0), A(16, 0), B(8,12) and C(0, 16).
| Corner points | Z = 22x1 + 18x2 |
| O(0, 0) | 0 |
| A(16, 0) | 352 |
| B(8, 12) | 392 |
| C(0, 20) | 360 |
The maximum value of Z occurs at B(8, 12).
∴ The optimal solution is x1 = 8, x2 = 12 and Zmax = 392
APPEARS IN
संबंधित प्रश्न
Find the feasible solution of the following inequation:
3x + 4y ≥ 12, 4x + 7y ≤ 28, y ≥ 1, x ≥ 0.
Find the feasible solution of the following inequation:
x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.
Solve the following LPP:
Maximize z = 4x1 + 3x2 subject to
3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0.
A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M1 and M2. A package of bulbs requires 1 hour of work on Machine M1 and 3 hours of work on M2. A package of tubes requires 2 hours on Machine M1 and 4 hours on Machine M2. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. If maximum availability of Machine M1 is 10 hours and that of Machine M2 is 12 hours, then formulate the L.P.P. to maximize the profit.
State whether the following statement is True or False:
LPP is related to efficient use of limited resources
Solve the following linear programming problem graphically.
Maximise Z = 4x1 + x2 subject to the constraints x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 and x1 ≥ 0, x2 ≥ 0.
Solve the following linear programming problem graphically.
Maximize Z = 60x1 + 15x2 subject to the constraints: x1 + x2 ≤ 50; 3x1 + x2 ≤ 90 and x1, x2 ≥ 0.
The values of θ satisfying sin7θ = sin4θ - sinθ and 0 < θ < `pi/2` are ______
The point which provides the solution of the linear programming problem, Max.(45x + 55y) subject to constraints x, y ≥ 0, 6x + 4y ≤ 120, 3x + 10y ≤ 180, is ______
The optimal value of the objective function is attained at the ______ of feasible region.
