1. [20 points] A mattress manufacturer has three production facilities located in Pittsburg (PA), Houston (TX), and Los Angeles (CA). They supply their products to three distribution centers in Boston (MA), Atlanta (GA), and San Jose (CA). Each distribution center has specific demands to meet. The capacity, demand, and transportation cost per unit between facilities are given in the following map: Demand = 1200 $5 $22 Capacity = 1100 Demand = 1100 $12 $24 $20 Capacity = 1000 Dates. $15 Demand = 800 $14 Capacity = 1300 For example, the capacity of Los Angeles facility is 1000 units. Demand of San Jose distribution center is 1100 units. Transportation cost per unit from Los Angeles to San Jose is $4. Develop a linear programming model defining the decision variables, objective function, and constraints. Using an appropriate linear programming solver, determine how many units should be shipped from each production facility to each distribution center to meet demand while minimizing transportation costs. Calculate the total transportation cost for this distribution plan. 2. [20 points] Javier Mendez is the head coach of the renowned AKA mixed martial arts gym. AKA has three full-time coaches already, each with years of experience in various martial arts. Their experience in martial arts in a scale of 1-5=, 1 being beginner and 5 being expert, is given in the following table: Martial Art Coach Boxing Wrestling Jui Jitsu Muay Thai Taekwondo MMA Derek Yuen 5 3 2 2 2 4 Wayne Phillips 2 4 5 IN IN Ron Kelsar 2 2 2 4 5 4 With the help of an MBA student, who is also a student at AKA, coach Mendez has developed a linear program to assign coaches to each martial arts class to maximize the overall teaching rating. The LPSolve model is given in 'Q2 Model.mod' file and Excel Solver Model is given in 'Q2 Model.xIsx'. In this model, the class rating is maximized (higher experience coach in a class is related to higher rating), while each coach will be teaching 2 classes or less and each class will have exactly one coach After developing the LP, coach Mendez hired three former champions as coaches to help with the increasing presence of athletes. The new coaches are also very experienced. Their rating is given in the table below: Martial Art Coach Boxing Wrestling Jui Jitsu Muay Thai Taekwondo MMA Daniel Cormier 4 5 3 2 2 4 Cain Velasquez 5 3 IN 5 Luke Rockhold 3 w 2 5 4 4 Coach Mendez wants to reduce the workload of coaches by assigning one coach to only one class. a. Develop a linear programming model stating the decision variables, objective function, and constraints to represent the problem. b. Solve the model for the previous situation (2 classes to 1 coach). Which coach should be assigned to what class? What is the total rating? (Hint: *.mod files can be opened with Notepad or similar text editor software in addition to LP Solve). C. Solve the model with the current situation (1 class to 1 coach). Modify the Linear Programming model and find the best assignment of 6 coaches to 6 classes to maximize the overall rating. Which coach should be assigned to what class? What is the total rating? d. If a coach can teach a maximum of 2 classes, would the solution change? Explain