#$3.$ Refrigeration Components. 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: MachineComponentShaperGrinder$164245342$The shaper is available for $120$ hours, and the grinder is available for $110$ hours. No more than $200$ units of component $3$ can be sold, but up to $1000$ 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 $3$ are $$8,$ $$6,$ and $$9,$ respectively. $($MLOs $3\mathrm{.}23\mathrm{.}5)$a$.$ Formulate and solve for the recommended production quantities.b$.$ What are the objective coefficient ranges for the three components? Interpret these ranges for company management.c$.$ What are the right$-$hand$-$side ranges? Interpret these ranges for company management.d$.$If more time could be made available on the grinder, how much would it be worth?e$.$If more units of component $3$ can be sold by reducing the sales price by $$4,$ should the company reduce the price?