A linear programming problem is as follows:
Maximize / minimize objective function z= 2x - y + 5 subject to constraints.
3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
If the comer points of feasible region are A(0, 10) B(12, 6) C(20, 0) 0(0, 0), then which of the following is true.
Answer & explanation
Correct answer: option 2
z = 2x - y + 5 → function
3x + 4y ≤ 60
x + 3y ≤ 30
x ≥ 0 , y ≥ 0 → solution in 1st quadrant
Corner points
Z(x, y) = 2x - y + 5
A(0, 10) so z(0, 10) = 2 × 0 - 10 + 5 = -10 + 5 = -5
B(12, 6) z(12, 6) = 2 × 12 - 6 + 5 = 24 - 6 + 5 = 23
C(20, 0) z(20, 0) = 20 × 2 - 0 + 5 = 40 + 5 = 45
D(12, 6) z(0, 0) = 0 - 0 + 5 = 5