$7.$ Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times $($in minutes$)$ required on each machine are as follows: Machine Component Shaper Grinder $164245342$ The shaper is available for $120$ hours, and the grinder for $110$ hours. No more than $200$ units of component $3$ can be sold, but up to $1,000$ units of each of the other components can be sold. In fact, the company already has orders for $600$ units of component $1$ that must be satisfied. The profit contributions for components $1,2,$ and are $$8,$ $$6,$ and $$9,$ respectively. a$.$ Formulate and solve for the recommended production quantities.