Imagine there are three technologies involved in manufacturing a certain product. The first technology requires $44$ unit$($s$)$ of labor and $22$ unit$($s$)$ of materials per unit of product. The second technology requires $33$ unit$($s$)$ of labor and $33$ unit$($s$)$ of materials. The third technology requires $22$ unit$($s$)$ of labor and $44$ unit$($s$)$ of materials.

What is the minimum cost of manufacturing the product if one unit of labor costs $$14$$$14$ and one unit of materials costs $$8$$$8?$ Write the exact answer. Do not round.

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Method $1$:$6060$ units of labor, $3030$units of capital$$

Method $2$: $7070$units of labor, $2020$units of capital$$

Method $3$: $4040$units of labor, $5050$units of capital

Step $1$ of $2$:

If hiring labor for the winter costs$$$$350$per unit$$350$per unit, and a unit of capital costs$$$$550,$$$550,$ what production method should the company choose?$$Select the best answer.