Question

A machine to manufacture fasteners has a setup cost of $1,400 and a unit cost of $0.008 for each fastener manufactured. A newer machine has a setup cost of $1,800 but a unit cost of only $0.0025 for each fastener manufactured. Find the break point. (Round your answer to the nearest whole unit.)

Answer 1

Given data:

First machine: setup cost of $1,400, unit cost $0.008

Newer machine: setup cost $1,800, unit cost $0.0025

Let x be the number of fasteners manufactured.

The first machine cost is:

`1,400+0.008x`

The newer machine cost is:

`1,800+0.0025x`

Equal the costs and solve x to find the break point:

`\begin{gathered} 1,400+0.008x=1,800+0.0025x \\ 0.008x-0.0025=1,800-1,400 \\ 0.0055x=400 \\ x=(400)/(0.0055) \\ \\ x=72,727 \end{gathered}`Then, the break point is at 72,727 fasteners manufactured