A cabinet shop produces and installs cabinets. Business is good, and the shop has an unlimited number of customers willing to pay $100 for each cabinet in - stalled. However, for the next month, the shop has only 1750 hr of labor and 1032 units of wood that it can commit for cabinet production. Each installed cabinet requires 5 hr of labor, 3 units of wood, and one frame. The frames can be prepared in the shop before installation, with each frame requiring 2 hr of the shop's labor and 1 unit of its wood, or they can be bought ready for instal - lation from the local mill for $27 each. The shop pays $6/hr for labor, $5/unit for wood, and only pays for the labor and wood used. For the next month, how many cabinets should the shop install, and how should the necessary frames be generated so that net income is maximized?
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