Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatures of $${160^0}C$$ and $${120^0}C$$ respectively. The plate has a constant thermal conductivity of $$200W/mK.$$

The location of maximum temp within the plate from left face is

Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatures of $${160^0}C$$ and $${120^0}C$$ respectively. The plate has a constant thermal conductivity of $$200W/mK.$$

The minimum temp within the plate in degree $$C$$ is

Capacities of production of an item over $$3$$ consecutive months in regular time are $$100,$$ $$100$$ and $$80$$ and in overtime are $$20,$$ $$20$$ and $$40.$$ The demands over those $$3$$ months are $$90,$$ $$130$$ and $$110.$$ The cost of production in regular time and overtime are respectively Rs. $$20$$ per item and Rs. $$24$$ per item. Inventory carrying cost is Rs. $$2$$ per item per month. The levels of starting and final inventory are nil. Backorder is not permitted. For minimum cost of plan, the level of planned production in overtime in the third month is

The maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continuous throughout the year. Ordering cost is Rs.$$100$$ per order and inventory carrying cost is Rs. $$10$$ per item per month. Annual cost (in Rs. ) of the plan, neglecting material cost, is