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 the given project network, where numbers along various activities represent the normal time. The free float on activity $$4$$-$$6$$ and the project duration, respectively, are

The actual sales of a product in different months of a particular year are given below:

The forecast of the sales, using the 4-month moving average method, for the month of February is ____________.

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 ________________.