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:

(B) and (C) only

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).