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 :
Answer & explanation
Correct answer: option 3
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)