Solve the following problem graphically:
Minimise and Maximise $Z=3x+9y$......$(1)$
subject to the constraints:
$x+3y \leq 60$.....$(2)$
$x+y \geq 10$......$(3)$
$x \leq y$.......$(4)$
$x \geq 0, y \geq 0$......$(5)$

• A
  Minimum value is $60$ at $(5,5)$ and maximum value is $180$ at all points on the line segment joining $(15,15)$ and $(0,20)$.
• B
  Minimum value is $90$ at $(0,10)$ and maximum value is $180$ at $(15,15)$.
• C
  Minimum value is $60$ at $(5,5)$ and maximum value is $180$ at $(0,20)$.
• D
  Minimum value is $30$ at $(10,0)$ and maximum value is $200$ at $(0,20)$.