Question 16 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Question 16 A student of class XII studying Mathematics comes across an incomplete question in a book. Maximise 𝑍=3𝑥+2𝑦+1 Subject to the constraints 𝑥≥0,𝑦≥0, 3𝑥+4𝑦≤12, He/ She notices the below shown graph for the said LPP problem, and finds that a constraint is missing in it: Help him/her choose the required constraint from the graph. The missing constraint is (A) 𝑥+2𝑦≤2 (B) 2𝑥+𝑦≥2 (C) 2𝑥+𝑦≤2 (D) 𝑥+2𝑦≥2Given Maximise 𝑍=3𝑥+2𝑦+1 Subject to the constraints 𝑥≥0,𝑦≥0, 3𝑥+4𝑦≤12, First, we plot 𝟑𝒙+𝟒𝒚=𝟏𝟐 Putting x = 0, y = 3. So, point is (0, 3) Putting y = 0, x = 4. So, point is (4, 0) Checking these two points in the graph Now, the other line passes through (1, 0) and (0, 2) Equation of that line is (𝒚 − 𝟎)/(𝒙 − 𝟏)=(𝟐 − 𝟎)/(𝟎 − 𝟏) 𝑦/(𝑥 − 1)=2/(−1) 𝑦/(𝑥 − 1)=−2 y = –2 (x – 1) y = –2x + 2 2x + y = 2 Now, it could be (B) 2𝑥+𝑦≥2 OR (C) 2𝑥+𝑦≤2 Since (2, 0) is in shaded region, it should satisfy the constraint Putting (2, 0) in (B) 2(2) +0≥2 4≥2 This is true Since the constraint is satisfied, Hence, 2𝑥+𝑦≤2 is our constraint So, the correct answer is (B)