Question

The objective function $z=x_1+x_2$, subject to $x_1+x_2\le 10,-2x_1+3x_2\le 15,x_1\le 6,x_1,x_2\ge 0$ has maximum value ______________ of the feasible region.

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

Answer 1

Answer: (C)

Given, objective function, $Z=x_1+x_2$ and constraints are
$x_1+x_2\le 10,-2x_1+3x_2\le 15,x_1\le 6,x_1,x_2\ge 0$

The point of intersection of lines $x_1+x_2=10$
and $-2x_1+3x_2=15$ is $B(3,7)$ 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
$O(0,0),A(0,6),B(3,7),C(6,4)$ and $D(6,0)$

At O(0, 0)	Z = 0 + 0 = 0
A(0, 6)	Z = 0 + 6 = 6
B(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 $C(6,4)$