Discussion
The optimal value of the LPP
Max : −4x + 5y,
Subject to :
y ≤ x and x ≤ 4
Answer: B
The optimal value is 4.
Since \(y \le x\),
\[ -4x + 5y \le -4x + 5x = x \le 4 \]
Both inequalities become equalities at \(x = y = 4\), which is feasible, so the maximum is exactly 4.
8 would need \(x = 8\), outside \(x \le 4\). 0 is the value at the origin, not the maximum. The bound above shows the objective cannot grow without limit, so an optimum does exist.
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