A company uses $$2555$$ units of an item annually. Delivery lead time is $$8$$ days. The recorder point (in number of units) to achieve optimum inventory is

In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ per month and the same is consumed at a rate of $$500$$ per month. The production and consumption continue simultaneously till the maximum inventory is reached. Then inventory is allowed to reduced to zero due to consumption. The lot size of production is $$1000.$$ If backlog is not allowed, the maximum inventory levels 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

A stockist wishes to optimize the number of perishable items he needs to stock in any month in his store. The demand distribution for this perishable item is: The stockist pays Rs.$$70$$ for each item and he sells each at Rs.$$90.$$ if the stock is left unsold in any month, he can sell the item at Rs.$$50$$ each. There is no penalty for unfulfilled demand. To maximize the expected profit, the optimal stock level is: