Reboot Incorporated is a manufacturer of hiking boots. Demand for boots is highly seasonal. In particular, the demand in the next year is expected to be $3,000,4,000,8,000,$ and $7,000$ pairs of boots in quarters $1,2,3,$ and $4,$ respectively. With its current production facility, the company can produce at most $6,400$ pairs of boots in any quarter. Reboot would like to meet all the expected demand, so it will need to carry inventory to meet demand in the later quarters. Each pair of boots sold generates a profit of $$20$ per pair. Each pair of boots in inventory at the end of a quarter incurs $$8$ in storage and capital recovery costs. Reboot has $1,000$ pairs of boots in inventory at the start of quarter $1.$ Reboot$$s top management has given you the assignment of doing some spreadsheet modeling to analyze what the production schedule should be for the next four quarters and making a recommendation.