Platypus wants to launch three, new hydration reservoir systems for day hikers. Senior management will limit introduction to only on system. DayTrek has an investment of $$139,000$ and over a four year period is projected to have sales $($beginning with year one and going to year four$)$ of $$47,400,$ $$60,250,$ $$68,500,$ and $$73,220.$ HikePak requires an investment of $$185,000,$ with forecasted sales of $$35,750,$ $$61,480,$ $$81,700,$ and $$89,900.$ HydraLite requires a $$112,785$ investment. Its sales are projected to be $$45,845,$ $$81,325,$ $$48,600,$ and $$46,350.$ Platypus uses an $8\mathrm{.}75\%$ cost of capital $($i$.$e$.,$ discount rate$).$

$(1)$ If Platypus uses cumulative cash flow, which product is chosen? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$(2)$ If Platypus uses the discounted cash flow analysis, what are the totals for the three different models?