Company X has a plant in Boston and ships all the products from there to its three market regions: the North, East, and West of the United States. The CEO has some potential locations in mind and wants to see if it is beneficial to build a new plant in these locations or not. The potential new locations are Los Angeles, Seattle, New York, and Denver. The production and transportation costs per product, the annual fixed cost for each plant, the annual demands for each region, and plant capacities are all shown in the table. North East West Boston $10 $12 $20 Los Angeles $15 $18 $8 Capacity 200,000 100,000 80,000 150,000 Fixed cost $5 million $1 million $0.9 million $1 million $1 million Seattle $6 $9 $5 New York $11 $6 $18 Denver $12 $15 $10 90,000 Demand 50,000 80,000 60,000 a) What is the current annual cost of company X, i.e., the annual cost of serving all the three regions by the Boston plant? b) Do you recommend adding any new plant(s)? If so, where should the plant(s) be built? How much the company would save per year by adding the new plant(s)? Assume that the Boston plant will be maintained at its current capacity but could be run at lower utilization. c) Assume that the CEO could design a new network from scratch (assume she did not have the Boston plant) and is considering the following options: (i) Build a plant in New York and ship all the products from the New York plant to the three regions. Build plants in Los Angeles and New York, and ship products to the North and East from the New York plant and to the West from the Los Angeles plant. Build plants in Denver and Los Angeles, and ship products to the West from the Los Angeles plant and to the East and North from the Denver plant. (iv) Build plants in Seattle, New York, and Denver, and ship products to the North from the Seattle plant, to the East from the New York plant, and to the West from the Denver plant. Which of these options are feasible (we need to meet all the demands)? What is the best choice among the feasible options? d) If the CEO could design a new network from scratch (again, assume she did not have the Boston plant but could built it at the cost and capacity specified in the table), where should company X locate its plants? What is the optimal quantity of products to ship from each plant to each of the market locations? What is the total cost? Write down the constraint you need to add based on the following assumptions (no need to solve the problem, just add the constraints to the Solver): e) All the five plants must be open. f) At least two plants must be open. g) At most three plants must be open. h) (Extra Credit) The Denver plant can only be open if the New York plant is open (i.e., if the New York plant is open, the Denver plant can be open or closed, but if the New York plant is closed, the Denver plant is definitely closed). Company X has a plant in Boston and ships all the products from there to its three market regions: the North, East, and West of the United States. The CEO has some potential locations in mind and wants to see if it is beneficial to build a new plant in these locations or not. The potential new locations are Los Angeles, Seattle, New York, and Denver. The production and transportation costs per product, the annual fixed cost for each plant, the annual demands for each region, and plant capacities are all shown in the table. North East West Boston $10 $12 $20 Los Angeles $15 $18 $8 Capacity 200,000 100,000 80,000 150,000 Fixed cost $5 million $1 million $0.9 million $1 million $1 million Seattle $6 $9 $5 New York $11 $6 $18 Denver $12 $15 $10 90,000 Demand 50,000 80,000 60,000 a) What is the current annual cost of company X, i.e., the annual cost of serving all the three regions by the Boston plant? b) Do you recommend adding any new plant(s)? If so, where should the plant(s) be built? How much the company would save per year by adding the new plant(s)? Assume that the Boston plant will be maintained at its current capacity but could be run at lower utilization. c) Assume that the CEO could design a new network from scratch (assume she did not have the Boston plant) and is considering the following options: (i) Build a plant in New York and ship all the products from the New York plant to the three regions. Build plants in Los Angeles and New York, and ship products to the North and East from the New York plant and to the West from the Los Angeles plant. Build plants in Denver and Los Angeles, and ship products to the West from the Los Angeles plant and to the East and North from the Denver plant. (iv) Build plants in Seattle, New York, and Denver, and ship products to the North from the Seattle plant, to the East from the New York plant, and to the West from the Denver plant. Which of these options are feasible (we need to meet all the demands)? What is the best choice among the feasible options? d) If the CEO could design a new network from scratch (again, assume she did not have the Boston plant but could built it at the cost and capacity specified in the table), where should company X locate its plants? What is the optimal quantity of products to ship from each plant to each of the market locations? What is the total cost? Write down the constraint you need to add based on the following assumptions (no need to solve the problem, just add the constraints to the Solver): e) All the five plants must be open. f) At least two plants must be open. g) At most three plants must be open. h) (Extra Credit) The Denver plant can only be open if the New York plant is open (i.e., if the New York plant is open, the Denver plant can be open or closed, but if the New York plant is closed, the Denver plant is definitely closed)