Productco produces three products. Each product requires labor, lumber, and paint. The resource requirements, unit price, and production cost (exclusive of raw materials) for each product are given in the table below. Currently, 900 labor hours, 1600 board feet of lumber and 1550 gallons of paint are available. Additional labor can be purchased at $6 per hour, additional paint at $2 per gallon, and additional lumber at $3 per board foot. Product Labor 1.5 3 2 123 Lumber Paint 3 2 2 2 3 4 Price ($) 26 28 31 Production Cost ($) 10 6 7 Productco established the following goals: Gl: Obtain a profit of at least 10500$ (any shortfall amount must be borrowed) G2: Purchase no additional labor G3: Purchase no additional lumber G4: Purchase no additional paint. Part A: Define the objective variables and write the constraints in mathematical format. For the next two parts use LINDO. Print and attach the source code and also write the answers on paper. Part B: Use non-preemptive goal programming to determine the optimal production schedule that best addresses these goals. Which goals are fully realized? Which ones are not fully realized and by how much? Part C: Use preemptive goal programming to determine the optimal production schedule using the following priority in decreasing order of importance: G1>G2>G3>G4. Which goals are fully realized? Which ones are not fully realized and by how much?