You are a manager on a fully automated factory building rocket engines. Each rocket engine requires multiple parts: $1$ unit of part A$,2$ units of part B and $4$ units of part C$.$ The cost of materials for each part is following: $$20$ for part A$,$ $$15$ for part B and $$10$ for part C$.$ You sell your rocket engines for $$300$ each.

You have two machines working for you $24$ hours per day, $7$ days a week. These machines can do any parts; however, they are not equally good in everything. Machine $1$ takes $3$ hours to make part A$,2$ hours to make part B$,$ and only $30$ minutes to make part C$.$ Machine $2$ takes $2$ hours to make part A$,1$ hour to make part B$,$ and $1$ hour to make part C$.$

As any manager you want to maximise your profit. How would you do that and how high it can go$?$

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