$($in minutes$)$ required on each machine are as follows:

$\backslash$table$[[$Machine$],[$Component$,$Shaper,Grinder$],[1,7,5],[2,5,5],[3,5,2]]$

The shaper is available for $125$ hours, and the grinder is available for $95$ hours. No more than $170$ units of component $3$ can be sold, but up to $1050$ units of each of the other components can be sold. In fact, the company already has orders for $625$ units of component $1$ that must be satisfied. The profit contributions for components $1,2,$ and $3$ are $$8,$$$6,$ and $$9,$ respectively.

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

Let $C_1=$ units of component $1$ manufactured

$C_2=$ units of component $2$ manufactured

$C_3=$ units of component $3$ manufactured

$\backslash$table$[[$Max$,C_1,+,C_2,+,C_3,,],[$s$.$t$,7C_1,+,C_2,+,C_3,,$Constraint $1],[C_1,+,C_2,+,2C_3,,$Constraint $2],[,,,,C_3,,$Constraint $3],[C_1,,,,,,$Constraint $4],[,,C_2,,,,,$Constraint $5],[C_1,,,,,,$Constraint $6]]$