Solve the following Linear Programming Problem graphically: Minimise: $Z = x + 2y$, subject to the constraints: $x + 2y \ge 100, \quad 2x - y \le 0, \quad 2x + y \le 200, \quad x, y \ge 0$.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 100 ##
The feasible region determined by the constraints, $x + 2y \ge 100$, $2x - y \le 0$, $2x + y \le 200$, $x, y \ge 0$, is given below.
$A(0, 50)$, $B(20, 40)$, $C(50, 100)$ and $D(0, 200)$ are the corner points of the feasible region.
The values of $Z$ at these corner points are given below.
|
Corner point |
Corresponding value of $Z=x+2y$ |
|
|
$A(0, 50)$ |
$100$ |
Minimum |
|
$B(20, 40)$ |
$100$ |
Minimum |
|
$C(50, 100)$ |
$250$ |
|
|
$D(0, 200)$ |
$400$ |
|