$($a$)$ Determine the capitalised cost at $3\mathrm{.}5\%$ interest of a manufacturing plant with an initial cost of $\pounds 1,750,000$ and annual operating and maintenance costs of $\pounds 28,000($payable at the end of each year$).$

$($b$)$ A manufacturing company wishes to compare possible replacement strategies for a machine which it purchases and maintains over a period. The initial cost of the machine, payable immediately, is $\pounds 100,000.$ Maintenance and other running costs are $\pounds 12,000,\pounds 15,000,\pounds 19,000,\pounds 25,000$ and $\pounds 40,000$ for the first, second, third, fourth and fifth years respectively, these amounts becoming due for payment at the end of the appropriate year. At the point of replacement, the machine would have a salvage value of $\pounds 30,000.$ The interest rate is $4\%$ p$.$a$.$ The company needs to decide whether to replace every $3$ years, every $4$ years or every $5$ years.

Based on capitalised costs, which replacement strategy should they adopt?