A manufacturer produces two types of products, $$1$$ and $$2,$$ at production levels of $${x_1}$$ and $${x_2}$$ respectively. The profit is given is$$2{x_1} + 5{x_2}.$$ The production constraints are $$$\eqalign{ & {x_1} + 3{x_2} \le 40 \cr & 3{x_1} + {x_2} \le 24 \cr & {x_1} + {x_2} \le 10 \cr & {x_1} > 0,\,{x_2} > 0 \cr} $$$

The maximum profit which can meet the constraints is

The sale of cycles in a shop in four consecutive months are given as $$70, 68, 82 95.$$ Exponentially smoothing average method with a smoothing factor of $$0.4$$ is used in forecasting. The expected number of sales in the next month is

A project consists of activities $$A$$ to $$M$$ shown in the net in the following figure with the duration of the activities marked in days.

The project can be completed

Market demand for springs is $$8,00,000$$ per annum. A company purchases these springs in lots and sells them. The cost of making a purchase order is Rs.$$1,200.$$ The cost of storage of springs is Rs.$$120$$ per stored piece per annum. The economic order quantity is