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?