Solve the following linear programming problem graphically :
Minimise $Z = 200 x + 500 y . . . (1)$
subject to the constraints:
$x + 2 y \geq 10 . . . (2)$
$3 x + 4 y \leq 24 . . . (3)$
$x \geq 0, y \geq 0 . . . (4)$ .

Open in App

Solution

The shaded region in Fig is the feasible region $A B C$ determined by the system of constraints $(2)$ to $(4)$ , which is bounded. The coordinates of corner points
Corner Point Corresponding value of $Z$
$(0, 5)$ $2500$
$(4, 3)$ $2300 \leftarrow M i n i m u m$
$(0, 6)$ $3000$
$A, B$ and $C$ are $(0, 5), (4, 3)$ and $(0, 6)$ respectively. Now we evaluate $Z = 200 x + 500 y$ at these points.
Hence, minimum value of $Z$ is $2300$ attained at the point $(4, 3)$ .

Suggest Corrections

Similar questions

Z = 3 x + 4 y

x + y \leq 4, x \geq 0, y \geq 0

Z = - 3 x + 4 y

x + 2 y \leq 8, 3 x + 2 y \leq 12, x \geq 0, y \geq 0

z = 3 x + 4 y

x + y \leq 4, x \geq 0, y \geq 0

Z = 3 x + 2 y

x + 2 y \leq 10, 3 x + y \leq 15, x, y \geq 0

Z = 3 x + 4 y

x + y \leq 4, x \geq 0, y \geq 0

Z = 4 x + y . . . (1)

x + y \leq 50 . . . (2)

3 x + y \leq 90 . . . (3)

x \geq 0, y \geq 0 . . . (4)

Join BYJU'S Learning Program