Question $5$

$0\mathrm{.}6pts$

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 $$13$ 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 $550$ hours of operation. It will take the operator

$30$ minutes to perform the necessary maintenance and will

require $$45$ 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: $1234\mathrm{.}56$