Question $20(2$ points$)$

A jumbo jet factory can produce two types of planes: UnitMach and BigMach. UnitMach takes $6$ weeks of labor and $7$ units of machine time. BigMach takes $8$ weeks of labor and $12$ units of machine time. The total weeks of labor available during the planning horizon are $50$; total units of machine time available during the planning horizon are $70.$ Contribution of UnitMach is $$10,000$ and BigMach is $$12,000.$ Assuming that integer quantities of products should be produced, find the total contribution maximizing solution.

Question $20$ options:

UnitMach $=8$ and BigMach $=0$

UnitMach $=8\mathrm{.}333$ and BigMach $=0$

UnitMach $=7$ and BigMach $=1$

UnitMach $=6$ and BigMach $=2$