a) The annual requirements for a particular raw material are 2,000 units, costing $ 1.00 each to the manufacturer. The ordering cost is $ 10.00 per order and the carrying cost is 16 % per annum of the average inventory value. Find the economic order quantity and the total cost of an inventory system. b) For an item, the production is instantaneous. The holding cost of one item is $ 1.00 per month and the set-up cost is $ 25 per run. If the demand is 200 units per month, find the optimum quantity to be produced per set-up and total cost of storage and set-up per month. c) A contract has a requirement for cement that amounts to 300 bags per day. No shortages are allowed. Cement costs $ 2.00 per bag, inventory carrying cost is 10 % of the average inventory valuation per day and it costs $ 20 to purchase order. Find the minimum cost of purchase quantity? d) The annual demand for a product is 100,000 units. The rate of production is 200,000 units per year. The set-up cost per production run is $5,000 and the variable production cost of each item is $ 10. The annual holding cost per unit is 20 % of its value. Find the optimum production lot-size and the length of the production run? e) A contractor undertakes to supply diesel engines to a truck manufacturer at a rate of 25 per day. He finds that the cost of holding a completed engine in stock is $ 16 per month, and there is a clause in the contract penalizing him $ 10 per engine per day late for missing the scheduled delivery date. Production of engines is in batches, and each time a new batch is started there are set-up costs of $ 10,000. How frequently should batches be started, and what should be the initial inventory level at the time each batch is completed?