If objective function for LPP is \(z=5x+7y\) and corner points of feasible region are (0, 0), (7, 0), (3, 4) and (0, 2) then maximum value of \(z\) occurs at :
(A) (0, 0)
(B) (7, 0)
(C) (3, 4)
(D) (0, 2)
(E) (4, 3)
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (C) Only
The maximum of z occurs at a corner point. Values of z = 5x + 7y at the corners:
\(z(0, 0) = 0\)
\(z(7, 0) = 35\)
\(z(3, 4) = 15 + 28 = 43\)
\(z(0, 2) = 14\)
So the maximum value of z is 43, reached only at (3, 4).
Checking the statements
(A) (0, 0) — Incorrect. z = 0 there, the smallest value.
(B) (7, 0) — Incorrect. z = 35 there, less than 43.
(C) (3, 4) — Correct. z = 43 there, the largest value.
(D) (0, 2) — Incorrect. z = 14 there, less than 43.
(E) (4, 3) — Incorrect. (4, 3) is not a corner point of the region (z there would be 41, less than 43).