Answer:
To find the maximum and minimum value of f=3x+y subject to x >/=0; 2x+y=6, we need to first solve the system of equations to find the feasible region.
From the equation 2x+y=6, we get y=6-2x. Substituting this into f=3x+y, we get f=3x+(6-2x)=6+x.
So, f is a linear function with slope 1. Since x >/=0, the feasible region is the line segment on the x-axis from x=0 to x=3.
To find the maximum value of f, we need to maximize x, which occurs at x=3. So, f(3)=6+3=9 is the maximum value of f.
To find the minimum value of f, we need to minimize x, which occurs at x=0. So, f(0)=6+0=6 is the minimum value of f.