A firm is specialized in building and selling family homes. the firm offers two basic models - A and B. Model A requires 4000 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 lumber. due to long lead times of supplies and manpower in the areafirm is forced to rely on existing supplies for upcoming building season. it has 400,000 hours of Labour, 150 tons of stone and 200,000 board feet lumber. what mix of model A and B houses should the firm construct if model A yields a profit of $3000 per unit and model B yields $6000 per unit. Assume that the firm will be able to sell all the units it builds.
1) formulate objective function and constraints
2) determine optimal quantities of model A and B and compute the resulting profit.
3) what is the optimum point
4) solve the equations for optimum points.