Free$-$response question $F$ is based on the following information: Flying

that produces parachutes. Flying Dog follows the Theory of Constraints management philosophy. The company has three production departments: Assembly, Testing, and Shipping.

Production runs $2,080$ hours per year $($you can also think of it as $124,800$ minutes per year if you prefer$).$ Flying Dog currently produces $5,200$ parachutes per year. Production capacity in each department is given below.

$\backslash$table$[[$Assembly Department,Testing Department,Shipping Department$],[5,200$ parachutes per year,$10,400$ parachutes per year,$12,480$ parachutes per year$]]$

Each parachute sells for $$450.$ Each parachute requires cloth for the canopy and thread for the suspension lines. Cloth costs $$100$ per parachute. Thread costs $$120$ per parachute.

Would Flying Dog benefit from a $$200,000$ annual investment in a machine that decreases the production time of the Assembly Department by four minutes per parachute? $($note that the time per parachute in the Assembly Department is currently $24$ minutes$).$ Supporty