Consider the linear programming problem (LPP):
Max Z= 4x + 3y
subject to the constraints:
x ≤ 8, y ≤ 4, x ≥ 0, y ≥ 0. At what coordinates will the objective function have optimal solution ?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → At the intersection of x - 8 = 0 and y - 4 = 0
The feasible region is the rectangle with corner points (0, 0), (8, 0), (8, 4) and (0, 4). The values of Z = 4x + 3y at the corner points are:
\( \displaystyle (0,\,0):\ Z=0 \)
\( \displaystyle (8,\,0):\ Z=32 \)
\( \displaystyle (8,\,4):\ Z=32+12=44 \)
\( \displaystyle (0,\,4):\ Z=12 \)
The maximum 44 is at (8, 4), the intersection of x − 8 = 0 and y − 4 = 0.