Use the table below to answer the following question$($s$).$

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?

The table below provides information on Letherin Hides boot design cost and production.

Letherin Hides $$

$$

Data $$

$$

$$ Summer Autumn Winter

Unit Production Cost $121315\mathrm{.}5$

Unit Inventory Holding Cost $1\mathrm{.}91\mathrm{.}91\mathrm{.}9$

Demand $200450500$

Use a linear optimization model based on the data to answer the following questions.

According to the linear optimization model, what is the total cost for the combind seasons if takes $3$ hours to design a boot?

$$17,000$

$$15,700$

$$24,200$

$$23,075$