Problem $8-23$

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:

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

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 $1000$ 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 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 $2$ manufacturid

$C_3=$ units of component $3$ manufactured

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

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