MHTCET 2016 Math Solved Paper

(c) Since, objective function is Z = x1+x2 and given constraints are
x1+x2 ≤ 10, −2x1+3x2 ≤ 15, x1 ≤ 6, x1,x2 ≥ 0.

Now, the point of intersection of lines x1+x2 = 10 and −2x1+x2 = 15 is B(3, 7) and pointof intersection of lines x1 = 6 and x1+x2 = 10 is C(6,4)
Here, 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 0(0,0)   Z = 0 + 0 = 0
At A(0,6)  Z= 0 + 6 = 6
At 5(3,7)  Z = 3 + 7 = 10
At C(6,4) Z = 6 + 4 = 10
AtD(6,0) Z = 6 + 0 = 6
Hence, Z is maximum at each point of the segment joining two points B(3,7) and C(6, 4)