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.

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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)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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