Step 1:
The objective function is $Z=3x-4y$
The corner points are $(0,0),(5,0),(6,5),(4,10),(0,8)$
For the points $(x,y)$ the objective function subject to $Z=3x-4y$
Step 2:
At $(0,0)$ the objective function $Z=3x-4y\Rightarrow Z=0$
At $(5,0)$ the objective function $Z=3x-4y\Rightarrow 3\times 5-4\times 0=15$
At $(6,5)$ the objective function $Z=3x-4y\Rightarrow 3\times 6-4\times 5=-2$
At $(6,8)$ the objective function $Z=3x-4y\Rightarrow 3\times 6-4\times 8=-14$
At $(4,10)$ the objective function $Z=3x-4y\Rightarrow 3\times 4-4\times 10=-28$
At $(0,8)$ the objective function $Z=3x-4y\Rightarrow 3\times 0-4\times 8=-32$
Step 3:
The maximum value of $Z$ is 15
The minimum value of $Z$ is -32
Hence the maximum value of $Z$+minimum value of $Z$ is $15-32=-17$
Correct option is $D$