The bounded feasible region for an LPP is shown as a shaded portion in the figure given below. The line CB is parallel to OA.
Then the minimum value of the objective function Z = 2x− 3y is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −38
The corner points are O(0, 0), A(5, 10), C(0, 6) and B.
CB is parallel to OA, so its slope is 2 and its equation is
\( \displaystyle y=2x+6 \)
At x = 5 this gives B(5, 16). The values of Z = 2x − 3y at the corners are:
\( \displaystyle Z(\mathrm{O})=0 \)
\( \displaystyle Z(\mathrm{A})=10-30=-20 \)
\( \displaystyle Z(\mathrm{B})=10-48=-38 \)
\( \displaystyle Z(\mathrm{C})=0-18=-18 \)
The minimum value is −38, at B(5, 16).