A manufacturer can produce $$12000$$ bearings per day. The manufacturer received an order of $$8000$$ bearings per day from a customer. The cost of holding a bearing in stock is Rs. $$0.20$$ per month. Setup cost per production run in Rs.$$500.$$ Assuming $$300$$ working days in a year, the frequency of production run should be

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 ________________.

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 ________.

Which one of the following is NOT correct?