Consider an objective function $$Z\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$ and the constraints
$$\eqalign{ & {x_1} + {x_2} \le 8, \cr & {x_1} + 2{x_2} \le 4, \cr & {x_1} \ge 0,{x_2} \ge 0, \cr} $$

The maximum value of the objective function is ________________.

Which one of the following is NOT correct?

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $$100 MPa.$$ If the yield, ultimate and corrected endurance strength of the shaft material are $$300$$ $$MPa,$$ $$500$$ $$MPa$$ and $$200$$ $$MPa,$$ respectively, then the factor of safety for the shaft is __________.

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $$0.2.$$ The dimensions shown in the figure are in mm. The braking torque (in $$N.m$$) for the brake shoe is ________.