A linear programming problem is as follows:
๐‘€๐‘–๐‘›๐‘–๐‘š๐‘–๐‘ง๐‘’ ๐‘ = 30๐‘ฅ + 50๐‘ฆ
subject to the constraints,
  3๐‘ฅ + 5๐‘ฆ ≥ 15
  2๐‘ฅ + 3๐‘ฆ ≤ 18
  ๐‘ฅ ≥ 0,๐‘ฆ ≥ 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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  1. Class 12
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Transcript

Question 33 A linear programming problem is as follows: ๐‘€๐‘–๐‘›๐‘–๐‘š๐‘–๐‘ง๐‘’ ๐‘ = 30๐‘ฅ + 50๐‘ฆ subject to the constraints, 3๐‘ฅ + 5๐‘ฆ โ‰ฅ 15 2๐‘ฅ + 3๐‘ฆ โ‰ค 18 ๐‘ฅ โ‰ฅ 0,๐‘ฆ โ‰ฅ 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 โ‰ฅ 15 2x + 3y โ‰ค 18 x โ‰ฅ 0 , y โ‰ฅ 0 โˆด Minimum of Z occurs at 2 points So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.