A manufacturer has identified the options for acquiring a machined part. It can make the part on a standard lathe for $250 per unit (including materials). It can make the part on a numerically controlled lathe for $150 per unit (including materials). It can make the part on a machining center for $50 per unit (also including materials). The manufacturer can acquire a standard lathe for $10,000. It could acquire a numerically controlled lathe for $100,000. A machining center would cost $350,000. It has also found that it can purchase the part for $350 per unit. What are the ranges in demand for which each method of procuring a part described above will be most economical?
What will be an ideal response?
If the quantity required is less than 100, purchase the part for $350 per unit. If the quantity needed is between 100 and 900, use the standard lathe. If the quantity needed is more than 900 but less than 2,500, use the numerically controlled lathe. If the quantity needed is greater than 2,500, the machining center is best.
Let D = Demand for the unit. Total costs:
Buy vs. Std: $350 × D = $10,000 + 250 × D; $100 × D = $10,000; D = 100
Std vs. NC: $250 × D + $10,000 = $150 × D + $100,000; $100 × D = $90,000; D = 900
NC vs. Machining Center: $150 × D + $100,000 = $50 × D + $350,000; $100 × D = $250,000; D = 2,500
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