Word Problem

Question

the set up 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 a larger machine that can produce the same plate at a cost of $0.20 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?Word problem

Answer 1

Assume the number of plates is P

 

The cost using the first machine is:

750 + .25*P

 

The cost of the second machine is:

1200 + .2*P

 

If we set these to be equal, we can find the number of plates where the costs will be the same:

 

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

.25P - .2P = 1200 - 750

.05P = 450

P = 450/.05

P = 9000 plates

 

So, after making 9000 plates, the total cost of using the second machine will be less.

 

Answer 2

Hi Rachel--

 

Since the difference in cost between the 2 machines is $450, we need to figure out how many more plates they will need to make in order to cancel out that 450.

 

The profit they would make on each plate on the larger machine would be 5 cents more than the profit for each made on the smaller one, so they can divide that 450 $ into little 5 cent pieces.

 

450 divided by .05 (or if you hate decimals, do 45000 cents divided by 5 cents per plate) =

 

9000 plates.

 

Hope this helps!

 

Matt in NY