3 - 1. LP formulation - Overtime 2 A company manufactures three products whose unit profits are $22, $25, and $23, respectively. The company has budgeted 80 hours of labor time and 65 hours of machine time for the production of the three products. The labor requirements per unit of products 1, 2 and 3 are 2, 1 and 2 hours, respectively. The corresponding machine time requirements per unit are 1, 1 and 2 hours. The company has weekly demand for each product; 10 for product 1, 50 for product 2, and 10 for product 3. The company regards the budgeted labor and machine hours as goals that may be exceeded, if necessary, but maximum labor overtime is up to 30 hours, and maximum machine overtime is up to 30 hours as well. For machine overtime, it costs $10 per additional machine hour. For labor overtime, there are 3 employees are available and it pays differently; $15 for John's additional hour, $17 for Bill's, and $20 for Cindy's. Each employee's overtime is up to 10 hours, so total will be 30 hours. a) Please formulate this problem as a LP. O MUST define the decision variables first! Then, identify the objective function and constraints. b) Solve the problem using LINDO or Solver and attach the output using Courier New font. c) Explain your production plan, such as amount of each product produced, each employee's labor overtime used, machine overtime used, and the total profit. No handwriting for model and outputs! No grade for handwriting! 3 - 2. LP formulation - Overtime 2 In addition to the problem 3-1, let's consider the following situation: If any employee needs to work for overtime, all other employee should work for same hours. How do you make additional constraint(s) for this restriction? How this restriction changes the decision? a) Please formulate this problem as a LP. MUST define the decision variables first! Then, identify the objective function and constraints. b) Solve the problem using LINDO or Solver and attach the output using Courier New font. c) Explain your production plan, such as amount of each product produced, each employee's labor overtime used, machine overtime used, and the total profit