A machine that produces a certain piece must be turned off by the operator after each piece is completed. The machine "coasts" for $15$ seconds after it is

turned off, thus preventing the operator from removing the piece quickly before producing the next piece. An engineer has suggested installing a brake that

would reduce the coasting time to $3$ seconds.

The machine produces $50,000$ pieces a year. The time to produce one piece is $1$ minute $45$ seconds, excluding coastint time. The operator earns $$10$ an hour

and direct costs for operation are $$5$ an hour. The direct costs are incurred whenever the operator has to work. The brake will require servicing every $589$

hours of operation. It will take the operator $30$ minutes to perform the necessary maintenance and will require $$48$ in parts and material. The brake is

expected to last $7,500$ hours of operation $($with proper maintenance$)$ and will have no salvage value.

How much could be spent for the brake if the Minimum Attractive Rate of Return is $10\%$ compounded annually?

Enter your answer in this format: $1234\mathrm{.}56$