1. A construction firm specializes in building and selling single-family homes. The firm offers two basic types of houses: model A and model B. Model A houses require 4,000 labor hours, 2 tons of stone, and 2000 board feet of lumber. Model B houses require 10000 labor hours, 3 tons of stone, and 2000 board feet of lumber. Due to long lead times for ordering supplies and the scarcity of skilled and semi-skilled workers in the area, the firm will be forced to rely on its present resources for the upcoming building season. It has 400000 hours of labor, 150 tons of stone, and 200000 board feet of lumber.
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3.  What mix of model A and B houses should the firm construct if model A yields a profit of $10000 per unit and model B yields a profit of $20000 per unit? Assume that the firm will be able to sell all the units it builds. Formulate the objective function and constraints.