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 :
Answer & explanation
Correct answer: option 4
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)