The corner points of the feasible region of a LPP are P(0, 5), Q(1, 5), R(4, 2) and S(12, 0). The minimum value of the objective function $Z=2x+5y $ is at the point :

R

Objective function: $Z = 2x + 5y$

Evaluate $Z$ at each corner point:

$Z(P) = 2*0 + 5*5 = 25$

$Z(Q) = 2*1 + 5*5 = 2 + 25 = 27$

$Z(R) = 2*4 + 5*2 = 8 + 10 = 18$

$Z(S) = 2*12 + 5*0 = 24 + 0 = 24$

Minimum value = 18 at point R(4, 2)

Answer: R(4, 2)