machine are as follows.

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.

$($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 $2$

component $3$

units

units

component $1$ $ to $

component $2$ to $

component $3$

to $