The corner points of the bounded feasible region of a linear programming problem are A(15,0), B(40,0), C(4, 18), D(6, 12) and objective function is z = 20 x + 10 y , then which of the following are TRUE ?
(A) Value of z at point A(15, 0) = 300.
(B) Value of z at point B(40, 0) = 800.
(C) Value of z at point C(4, 18) = 340.
(D) Maximum value of z = 800.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
For a bounded feasible region, the maximum of z occurs at a corner point. At the corner points, z = 20x + 10y is
\( \displaystyle A(15,\,0):\ z=300 \)
\( \displaystyle B(40,\,0):\ z=800 \)
\( \displaystyle C(4,\,18):\ z=80+180=260 \)
\( \displaystyle D(6,\,12):\ z=120+120=240 \)
So z = 300 at A, 800 at B, 260 at C and 240 at D, and the maximum value of z is 800.
Checking the statements
(A) Value of z at point A(15, 0) = 300. — Correct. 20 × 15 + 10 × 0 = 300.
(B) Value of z at point B(40, 0) = 800. — Correct. 20 × 40 + 10 × 0 = 800.
(C) Value of z at point C(4, 18) = 340. — Incorrect. z = 80 + 180 = 260 at C.
(D) Maximum value of z = 800. — Correct. 800 is the largest of the corner values 300, 800, 260 and 240.