Which of the following statements are correct in reference to the linear programming problem(LPP): Maximize $Z = 5x + 2y$ subject to the following constraints $3x+5y≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0$.
(A) The LPP has a unique optimal solution at (2, 0) only.
(B) The feasible region is bounded with corner points (0, 0), (2, 0), (20/19, 45/19) and (0, 3).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
Given LPP
Maximize $Z=5x+2y$
Subject to
$3x+5y\le15$
$5x+2y\le10$
$x\ge0,\;y\ge0$
Hence feasible corner points are
$(0,0),\;(2,0),\;\left(\frac{20}{19},\frac{45}{19}\right),\;(0,3)$
Evaluate $Z$
$Z(0,0)=0$
$Z(2,0)=10$
$Z\left(\frac{20}{19},\frac{45}{19}\right)=10$
$Z(0,3)=6$
Maximum value is $10$ and it occurs at infinitely many points on the segment joining $(2,0)$ and $\left(\frac{20}{19},\frac{45}{19}\right)$
(A) False
(B) True
(C) True
(D) False
The correct statements are (B) and (C).