Deterministic Age Replacement Strategies

QUESTION $3$:

For the basic age replacement model, consider a piece of equipment that costs $$18,000$ to replace. The

total maintenance costs for five years of operation are estimated to be $$2,400.$ Assuming a linear

maintenance cost rate, find the value of a and the optimal age at which the equipment should be

replaced.

$($Production and Operation Analysis by Steven Nahmias, $7$th edition, pg$\mathrm{.}774$ Problem # $21)$