A linear programming problem (
LPP
) along with the graph of its constraints is shown below.
The corresponding objective function is: Z=18x+10y, which has to be minimized. The smallest value of the objective function Z is 134 and is obtained at the corner point (3,8),
The optimal solution of the above linear programming problem ____.
(A) does not exist as the feasible region is unbounded.
(B) does not exist as the inequality 18x+10y<134 does not have any point in common with the feasible region.
(C) exists as the inequality 18x+10y>134 has infinitely many points in common with the feasible region.
(D) exists as the inequality 18x+10y<134 does not have any point in common with the feasible region.
Question 16 A linear programming problem ( 𝐋𝐏𝐏 ) along with the graph of its constraints is shown below. The corresponding objective function is: 𝑍=18𝑥+10𝑦, which has to be minimized. The smallest value of the objective function Z is 134 and is obtained at the corner point (3,8), The optimal solution of the above linear programming problem ____. (A) does not exist as the feasible region is unbounded. (B) does not exist as the inequality 18𝑥+10𝑦<134 does not have any point in common with the feasible region. (C) exists as the inequality 18𝑥+10𝑦>134 has infinitely many points in common with the feasible region. (D) exists as the inequality 18𝑥+10𝑦<134 does not have any point in common with the feasible region.Since the feasible region is unbounded,
Hence, 134 may or may not be the minimum value of Z
So, we need to graph inequality :
Z < 134
18x + 10y < 134
The graph of is 18x + 10y < 134 given
As, there is no common points between the feasible region and the inequality.
∴ Min Z = 134 at (3, 8)
So, the correct answer is (D)
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Davneet Singh
Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.
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