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

Consider the following data for an item.
Annual demand: $$2500$$ units per year Ordering cost: Rs.100 per order Inventory holding rate: $$25\% $$ of unit price. The optimum order quantity (in units) is:

Price quoted by a supplier

The optimum order quantity (in units) 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:

The distribution of lead-time demand fro an item is as follows:

The reorder level is $$1.25$$ times the expected value of the lead-time demand. The service level is