Exercise $4-49($Static$)$ Theory of Constraints $($LO $4-5)$

Leach Finishing makes various metal fittings for the construction industry. Three of the fittings, models X$-12,$ X$-24,$ and X$-30,$ require grinding on a patented machine of which Leach has only one. The cost of production information for the three products follow:

$$

$$X$-12$X$-24$X$-30$Price per fitting$ $27$$ $43$$ $62$Variable cost per fitting$ $12$$ $19$$ $36$Units per hour of grinding$1812\mathrm{.}510$

$$

The testing machine used for both models has a capacity of $2,750$ hours annually. Fixed manufacturing costs are $$480,000$ annually.

$$

Required:

a$.$ Suppose that Leach Finishing can sell at most $54,400$ units of any one fitting. How many units of each fitting model should Leach Finishing produce annually?

b$.$ Suppose that Leach Finishing can sell at most $14,400$ units of any one fitting. How many units of each fitting should Leach Finishing produce annually?