A machine is purchased for 3600. The annual running cost of the machine is initially 1800, but

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A machine is purchased for £3600. The annual running cost of the machine is initially £1800, but rises annually by 10%. After x years its secondhand value is £3600e–0.35x. Show that the average annual cost £C (including depreciation) after x years is given by

3600(1-e-0.35x) X C =- +90(19 + x)

Show graphically that the machine should be replaced after about 4 years, and use an iterative method to refine this estimate.

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