$30-$ BuildPro Contractors, a major player in the construction industry, is preparing for a large$-$scale infrastructure project that requires the purchase of new heavy$-$duty excavation equipment. Two suppliers have submitted bids, each offering equipment with different cost structures and features. Supplier X proposes equipment with an initial cost of $$45,000,$ an annual maintenance and operation $($M&O$)$ cost of $$6,000$ per year, and a salvage value of $$7,000$ at the end of its $8-$year useful life. Supplier Y offers equipment priced at $$50,000,$ with lower annual M&O costs of $$5,500$ per year and a higher salvage value of $$9,000$ at the end of its $10-$year useful life. BuildPro$$s financial team evaluates investments using a MARR of $15\%$ per year. Additionally, for projects with flexible timelines, BuildPro prefers to conduct evaluations over a fixed $7-$year study period, regardless of the equipment's actual useful life.

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$$ i$.$ Calculate the present worth cost for each supplier$$s equipment over their respective useful lives. Which option should BuildPro choose?

$$ ii$.$ Using a $7-$year study period for evaluation and assuming salvage values remain constant, which supplier$$s equipment would be the better choice?