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

$164$

$245$

$342$

The shaper is available for $120$ hours, and the grinder for $110$ hours. No more than $250$ units of component $3$ can be sold, but up to $1,000$ units of component $1$ and up to $1,000$ units of component $2$ can be sold. In fact, the company already has orders for $550$ units of component $1$ that must be satisfied. The per unit selling price and per unit variable costs for each of the three components are as follows: