Letherin Hides is a company that makes boots specifically targeting college students. Forecasts of sales for the next year are $200$ in the summer, $450$ in the autumn, and $500$ in the winter. Accessories that are used on the boots are purchased from a supplier for $$31\mathrm{.}66.$ The cost of capital is estimated to be $24\%$ per year $($or $6\%$ per quarter$)$; thus, the holding cost per item is $0\mathrm{.}06($$$31\mathrm{.}66)=$ $$1\mathrm{.}9$ per quarter $($rounded figure$).$ Letherin Hides hires freelance art designers at part$-$time to craft designs during the summer, and they earn $$6$ per hour. In the autumn, labor is more difficult to keep, and the owner must pay $$6\mathrm{.}5$ per hour to retain qualified help. Because of the high demand for part$-$time help during the winter holiday season, labor rates are higher in the winter, and workers earn $$7\mathrm{.}75$ per hour. Each boot design takes $2$ hours to complete. How should production be planned over the three quarters to minimize the combined production and inventory holding costs?