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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

A linear programming problem is as follows:
π‘€π‘–π‘›π‘–π‘šπ‘–π‘§π‘’ 𝑍 = 30π‘₯ + 50𝑦
subject to the constraints,
Β  3π‘₯ + 5𝑦 β‰₯ 15
Β  2π‘₯ + 3𝑦 ≀ 18
Β  π‘₯ β‰₯ 0,𝑦 β‰₯ 0
In the feasible region, the minimum value of Z occurs at

(a) a unique pointΒ  Β  Β  Β  Β  Β  Β (b) no point

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

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Transcript

Question 33 A linear programming problem is as follows: π‘€π‘–π‘›π‘–π‘šπ‘–π‘§π‘’ 𝑍 = 30π‘₯ + 50𝑦 subject to the constraints, 3π‘₯ + 5𝑦 β‰₯ 15 2π‘₯ + 3𝑦 ≀ 18 π‘₯ β‰₯ 0,𝑦 β‰₯ 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 β‰₯ 15 2x + 3y ≀ 18 x β‰₯ 0 , y β‰₯ 0 ∴ Minimum of Z occurs at 2 points So, the correct answer is (d)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.