A linear programming problem is as follows:
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = 30𝑥 + 50𝑦
subject to the constraints,
  3𝑥 + 5𝑦 ≥ 15
  2𝑥 + 3𝑦 ≤ 18
  𝑥 ≥ 0,𝑦 ≥ 0
In the feasible region, the minimum value of Z occurs at

(a) a unique point             (b) no point

(c) infinitely many points  (d) two points only

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Transcript

Question 33 A linear programming problem is as follows: 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = 30𝑥 + 50𝑦 subject to the constraints, 3𝑥 + 5𝑦 ≥ 15 2𝑥 + 3𝑦 ≤ 18 𝑥 ≥ 0,𝑦 ≥ 0 In the feasible region, the minimum value of Z occurs at (a) a unique point (b) no point (c) infinitely many points (d) two points only Our LPP is Minimise Z = 5x + 3y Subject to 3x + 5y ≥ 15 2x + 3y ≤ 18 x ≥ 0 , y ≥ 0 ∴ Minimum of Z occurs at 2 points So, the correct answer is (d)

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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.