Solve the following linear programming problem graphically :
Maximize $z = 60 x + 15 y$ subjected to constraints:
$x + y \leq 50$
$3 x + y \leq 90$
$x, y \geq 0$

Open in App

Solution

Maximize $z = 60 x + 15 y$
$x$ $0$ $50$ $30$
$y$ $50$ $0$ $20$
$x + y \leq 50$
$3 x + y \leq 90$
$x$ $0$ $30$ $10$
$y$ $90$ $0$ $60$
$x, y \geq 0$

$3 x + y = 90 x + y = 50_________2 x = 40$
$x = 20$
$y = 30$
Optimal solution $= 60 x + 15 y$
$= 60 (20) + 15 (30)$
$= 1200 + 450$
$= 1650$

Suggest Corrections

Similar questions

z = 3 x + 4 y

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

x + y \leq 50 3 x + y \leq 90 x, y \geq 0

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 + 2 y

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