on each machine are as follows:

$\backslash$table$[[,$Machine$],[$Component$,$Shaper,Grinder$],[1,6,4],[2,4,5],[3,4,2]]$

$($a$)$ Formulate and solve for the recommended production quantities.

component $1$ units

component $2$ units

component $3$ units

component $1$ to units

component $2$ to units

component $3$ to units

Interpret these ranges for company management.

Changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce.

Changes in the profit coefficients outside these ranges will not cause a change in the optimal number of components to produce.

Changes in the profit coefficlents within these ranges will cause changes in the optimal number of components to produce.