The production department for an aluminum valve plant is scheduling its work for next month. Each valve must go through three separate machines during the fabrication process. After fabrication, each valve is inspected by a human being, who spends 15 minutes per valve. There are 525 inspection hours available for the month. The time required (in hours) by each machine to work on each valve is shown in the following table. Also shown are the minimum number of valves that must be produced for the month and the unit profit for each valve.
Determine the optimal production mix for the valve plant to make the best use of its profit potential.

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PRODUCT V23 V24 V78 V906 (HOURS) Drilling 0.40 0.30 0.45 0.35 700 Milling 0.60 0.65 0.52 0.48 890 Lathe 1.20 0.60 0.5 0.70 1,200 Unit profit $16 $12 $13 S8 Minimum 200 250 600 450