(a) Write the linear programming (LP) model that could be used to find the best solution (clearly define the decision variables and any other notations you use in your model, show the necessary set of algebraic expressions for the constraints and the objective function, and label the units and the purpose of each constraint and the objective function) (b) Use an LP software to solve your model and submit the input file you used (c) Write out the final solution 5-5. You are an engineer working for a construction firm that plans to build an apartment complex. You have a choice of building some combination of one-, two-, and threebedroom apartments. A one-bedroom apartment requires 1000 board ft of lumber, 10 yd d3 of concrete, and 20 rolls of insulation. A two-bedroom apartment requires 1400 board ft of lumber, 12yd3 of concrete, and 24 rolls of insulation. A three-bedroom apartment requires 1600 board ft of lumber, 13 yd 3 of concrete, and 26 rolls of insulation. A onebedroom apartment rents for $250 per month, a two-bedroom apartment for $300 per month, and a three bedroom for $325 per month. Local ordinances require at least one three-bedroom apartment for every three onc-and-two bedroom apartments. Your firm has set aside 100,000 board ft of lumber, 1200yd3 of concrete, and 2500 rolls of insulation for this project. Formulate this as a linear programming problem to maximize rental income. Give objective function and constraints