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 is available for $110$ hours. No more than $200$ units of component $3$ can be sold, but up to $800$ 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 per unit selling price and per unit variable costs for each of the three components are as follows.

Component Selling Price Material Cost Labor Cost

$1$ $$25$ $$12$ $$5$

$2$ $$18$ $$8$ $$4$

$3$ $$27$ $$13$ $$5$

$($a$)$

For each component, calculate the profit margin $($in dollars, profit margin $=$ selling price $$ material cost $$ labor cost$).$

component $1$ $

component $2$ $

component $3$ $

Formulate and solve for the recommended production quantities that will maximize contribution to profit.

component $1$ units

component $2$ units

component $3$ units

$($b$)$

What are the objective coefficient ranges $($in dollars$)$ for the three components? $($If there is no upper or lower limit$,$ enter NO LIMIT. Round your answers to two decimal places.$)$

component $1$ $ to $

component $2$ $ to $

component $3$ $ to $

$($c$)$

What are the right$-$hand$-$side ranges? $($Use minutes for time. If there is no upper or lower limit$,$ enter NO LIMIT. Round your answers to the nearest integer.$)$

shaper availability to

grinder availability to