A construction contractor builds single-family dwellings and apartment buildings. The contractor can make ($ 5000) profit on

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A construction contractor builds single-family dwellings and apartment buildings. The contractor can make \(\$ 5000\) profit on each house and \(\$ 50,000\) on each apartment. It takes 400 hours to build a house and 1000 hours to build an apartment. Each house requires 1600 cubic feet of concrete, and each apartment requires 3000 cubic feet of concrete to lay the foundation. Bricks are the only other limiting resource; houses require 20,000 square feet and apartments require 100,000 square feet of brickface. A total of 10,000 hours, 60,000 cubic feet of concrete, and \(1,000,000\) square feet of brick are available. Find the numbers of single-family dwellings and apartments that should be made to maximize the contractor's profit.

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