A small 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 2,000 board feet of lumber. Model B houses require 10,000 labor hours, 3 tons of stone, and 2,000 board feet of lumber. Due to long lead times for ordering supplies and the scarcity of skilled and semiskilled workers in the area, he firm will be forced to rely on its present resources for the upcoming building season. It has 400,000 hours of labor, 10 tons of stone, and 200,000 board feet of lumber. Model A houses are expected to yield a profit of $3,000 per unit and Model B houses a profit of $6,000 per unit.
Write the LP formulation to help the firm determine the best mix of model A and B houses to build.