A manufacturer has to supply N items per month at a uniform daily rate. Each time a production run is started it costs £c₁, the ‘set-up’ cost. In addition, each item costs £c₂ to manufacture. To avoid unnecessarily high production costs, the manufacturer decides to produce a large quantity q in one run and store it until the contract calls for delivery. The cost of storing each item is £c₃ per month. What is the optimal size of a production run?