The setup cost of a machine that mills brass plates is $750. After setup, it costs $0.25 to mill each plate. Management is considering the purchase of larger machine that can produce the same plate at a cost of $0.25 per plate. If the setup cost of the larger machine is $1,200, how many plates would the company have to produce to make the purchase worthwhile?

Question

Jeremy Woods

Mathematics

12 March, 16:11

The setup cost of a machine that mills brass plates is $750. After setup, it costs $0.25 to mill each plate. Management is considering the purchase of larger machine that can produce the same plate at a cost of $0.25 per plate. If the setup cost of the larger machine is $1,200, how many plates would the company have to produce to make the purchase worthwhile?

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Christine Erickson · Answer 1

Hi there,

They would have 9000 plates in all. Here’s how ...

750 +.25*P = 1200 +.2*P

.25P -.2P = 1200 - 750

.05P = 450

P = 450/.05

P = 9000 plates

The cost of the second machine is going to be 1200 +.2*P. And for the first it is going to be 750 +.25*P. So they will have 9000 plates in all