Minimise $Z=13x−15y$ subject to the constraints: $x+y≤7,2x−3y+6≥0,x≥0,y≥0$.

-30

The correct answer is Option (1) → -30

Convert inequalities to equations

$x + y = 7$

Intercepts:

• $x=7, y=0$

• $x=0, y=7$

$2x - 3y = -6$

Intercepts:

• $x=0⇒y=2$

• $y=0⇒x=−3$ (outside first quadrant, but line is still drawn)

The shaded region shown as $OABC$ is bounded and coordinates of its corner points are (0, 0), (7, 0), (3, 4) and (0, 2), respectively.

Hence, the minimum value of Z is −30 at (0, 2).