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.

Minimum value of z is - 5

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