The objective function `z = x_1 + x_2`, subject to `x_1 + x_2 leq 10,-2x_1 + 3x_2 leq 15,x_1 leq 6,x_1 ,x_2 leq 0` has maximum value of the feasible region.

Options

A. at only one point
B. at only two points
C. at every point of the segment joining two points
D. at every of the segment joining two equivalent to'

Answer

C

Explanation

Given objectie function `Z=x_(1)+x_(2) and `constraints are `x_(1)+x_(2) le 10, -2x_(1)+3x_(2) le 15, x_(1) le 6, x_(2) ge0`.

The point of intersection of lines `x_(1) + x_(2)=10` and `-2x_(1) + 3x_(2)=15` is 8(3, 7) and point of intersection of lines `x_(1)= 6 and x_(1)+x_(2)= 10` is C(6, 4).
The feasible region is OABCD. The corner points of the feasible region are
O(0, 0), A(0, 6), 8(3, 7), C{6, 4) an.d 0(6, 0).

Hence, Z is maximum at every point of the segment combined two points
B (3,7) and C(6,4).