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A firm has an annual demand of \(S\) units for a good whose purchase cost is \(f c\) per unit. Each order costs \(£ a\) to place, and the cost of holding stock is \(b \%\) of the average value of stock per annum. Determine the optimal order quantity.

A local firm uses 2000 units of a particular component each year. The component has a purchase price of \(£ 4 /\) unit, while the cost of holding stock is estimated at \(20 \%\) of the average stock value. If the cost of placing each order is \(£ 12.50\), find the optimal number of orders placed each year. Suppose the component supplier offers a discount of \(2 \%\) on the purchase price if orders are placed in units of 1000 . Is the discount worth accepting?
Suppose that instead of a single figure you had been given a probability distribution for the number of units used each year. Indicate the effect on stock policy.
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