If the comer points of the feasible region for an L.P.P. are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function $\mathrm{F} = 4\mathrm{x} + 6\mathrm{y}$ occurs at

$\mathrm{F} = 4\mathrm{x} + 6\mathrm{y}$

At  $(0,2),\mathrm{F}=4\times 0+6\times 2=12\to$Minimum

At $(3,0),F=4\times 3+6\times 0=12\to$Minimum

At $(6,0),F=4\times 6+6\times 0=24$

At $(6,8),F=4\times 6+6\times 8=72\to$Maximum

At $(0,5),F=4\times 0+6\times 5=30$. 

Since minimum of F occurs at (0, 2) and (3, 0). It means minimum value of F occurs at every point on the line segment joining the points (0, 2) and (3, 0).

$\therefore$ Option (d) is the correct answer.