A metallic cylindrical casing of an exhaust pipe has inner radius $$50$$ $$mm$$ and wall thickness $$7$$ $$mm.$$ If the thermal conductivity of the material of the casing is $$50$$ $$W/m$$-$$K,$$ then the thermal resistance of the casing in $$K/kW$$ is ________________ (up to three decimal places).

An electrical appliances showroom sells $$2,400$$ ceiling fans in one year ($$52$$ weeks). The holding cost is $$10\% $$ of the cost of the ceiling fan. The most of one ceiling fan is Rs. $$600$$. The cost incurred for placing an order is Rs. $$201.$$ There is a lead time of $$5$$ weeks. The economic order quantity $$(EOQ)$$ and the reorder level, respectively (rounded to the next higher integer) are

The potential production alternatives for manufacturing a product along with their unit cost and monthly capacity are given in the Table.

The inventory at the end of july is $$100$$ units. If the demand for the month of August is $$620,$$ then the minimum total cost (in Rs.) to meet the demand is ______________

In a project, tasks $$A, B, C, D, E, F, G, H, I$$ and $$J$$ are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.

The time required (in days) to complete the project along the critical path is ______________