The function

$Z= \alpha x + \beta y (\alpha , \beta > 0)$

corresponds to the objective function of an LPP that needs to be maximized subject to

$x+ y ≤ 1, x, y > 0. $ Then the set of optimal solutions is :

{(t, 1-t) : t ∈ [0, 1]} if $\alpha = \beta $

The correct answer is Option (4) → $\{(t, 1-t) : t ∈ [0, 1]\}$ if $\alpha = \beta$

corner points → (0, 0), (0, 1), (1, 0)

$Z= \alpha x + \beta y$

if $α=β$

$Z_{max} = α=β$ at (0, 1) and (1, 0)