Q135 / 240 · KCET 2026 · Mathematics

In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is

  • A
    $1$
  • B
    $2$
  • C
    $0$
  • Correct answer
    D
    Infinity

Solution

According to the Fundamental Theorem of Linear Programming, if the optimal value of the objective function occurs at two distinct corner points of the feasible region, it also occurs at all points on the line segment joining these two points.

Since a line segment contains an infinite number of points, the maximum value $Z_{max}$ occurs at infinitely many points.

Answer: Infinity

Hence, the correct answer is option: 'D'.

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