If line joining points A and B having position vectors 6a - 4b + 4c and - 4c respectively and the line joining the points C and 0 having position vectors - a - 2b - 3c and a + 2b - 5c intersect, then point of intersection is
B
C
D
A
Direction ratios of the line which is perpendicular to the lines with direction ratios - 1, 2, 2 and 0, 2, 1 are
1, 1, 2
2, - 1, 2
- 2, 1, 2
2, 1, - 2
The objective function Z = x1 + x2, subject to the constraints are x1 + x2 10, - 2x1 + 3x2 15, x1 6, x1x2 0 has maximum value of _ the feasible region.
at only one point
at only two points
at every point of the segment joining two points
at every point of the line joining two points equivalent to
C.
at every point of the segment joining two points
Given, objective function, Z = x1 + x2, and constraints are
x1 + x2 10, - 2x1 + 3x2 15, x1 6, x1x2 0
The point of intersection of lines x1 + x2 = 10 and - 2x1 + 3x2 = 15 is B(3, 7) and point of intersection of lines x1 = 6 and x1 + x2 = 10 is C(6,4).
The feasible region is 0A8C0. The corner points of the feasible region are O(0, 0), A(0, 6), 8(3, 7), C(6, 4) and 0(6, 0).
At O(0, 0) | Z = 0 + 0 = 0 |
A(0, 6) | Z = 0 + 6 = 6 |
A(3, 7) | Z = 3 + 7 = 10 |
C(6, 4) | Z = 6 + 4 = 10 |
D(6, 0) | Z = 6 + 0 = 6 |
Hence, Z is maximum at every point of the segment combined two points B(3,7) and C(6, 4)