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The maximum and the minimum values of 5x + 7y, when |x| + |y| ≤ 1 are

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. 5 and -5
  2. 5 and -7
  3. 7 and -5
  4. 7 and -7

Answer (Detailed Solution Below)

Option 4 : 7 and -7
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Detailed Solution

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Explanation:

Here Corner's points are

(1, 0), (0, 1), (-1, 0) & (0, -1)

Let z = 5x + 7y, so

z(1, 0) = 5, z(0, 1) = 7, z(-1, 0) = - 5, z(0, -1) = -7

Hence maximum value is 7 and minimum is -7
Option (4) is true

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