The corner points of the bounded feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If maximum value of \(z = ax + by\), where \(a,b \gt 0\), occurs at both (2, 4) and (4, 0) then
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(a= 2b\)
If the maximum occurs at both (2, 4) and (4, 0), z must have the same value at both points:
\(2a + 4b = 4a\)
\(4b = 2a\)
\(a = 2b\)
This is indeed the maximum: with a = 2b, z = 8b at (2, 4) and (4, 0), while z = 0 at (0, 0) and z = 5b at (0, 5).