Your firm produces specialized plastic moldings using an extruder machine. Demand for the moldings is steady throughout the year at 10,000 units per year. In its most efficient, “fast” mode, the extruder machine produces moldings at the rate of 15,000 per year, and a cost of $10.00 per molding. You figure your holding cost per unit per year to be

h = $2 + (5%)(unit production cost).

The extruder also has a slightly less efficient, “slow” production mode, in which it produces moldings at a rate of 11,000 units per year, and a unit cost of $10.10 per molding. The factory floor manager argues that this mode should not be used because the unit cost per molding is slightly higher than the fast mode, but the cost of setting up a production run is the same: $500 in both cases.

What mode should you run the machine in, and how long should your production runs be?