Make sure to identify and define the decision variables, and formulate the objective function and constraints for each problem. Please make it brief and understandable. Please answer each sub-questions a-e

Sleekfon and Sturdyfon are two major cell phone manufacturers that have recently merged. Their current market sizes are shown in Table 3. All demand is in millions of units. Sleekfon has three production facilities in Europe (EU), North America, and South America. Sturdyfon also has three production facilities in Europe (EU), North America, and the rest of Asia. The capacity (in millions of units), annual fixed costs (in millions of $), and variable production costs ($ per unit) for each plant are as shown in Table 4. Transportation costs are shown in Table 5. All transportation costs are shown in dollars per unit. Duties are applied on each unit based on the fixed cost per unit capacity, variable cost per unit, and transportation cost. Thus, a unit currently shipped from North America to Africa has a fixed cost per unit of capacity of $5.00 (=100/20 from Table 4), a variable production cost of $5.50, and a transportation cost of $2.20. The 25 percent import duty is thus applied on $12.70 (5 + 5.50 + 2.20) to give a total cost on import of $15.88. For the questions to follow, assume that the market demand is as in Table 3. The merged company has estimated that scaling back a 20-million-unit plant to 10- million unit saves 30 percent in fixed costs. Variable costs at a scaled-back plant are unaffected. Shutting a plant down (either 10 million or 20 million units) saves 80 percent in fixed costs. Fixed costs are partially recovered because of severance and other costs associated with a shutdown.

a. What is the lowest cost achievable for production and distribution networks prior to the merger? Which plants serves which markets?

b. What is the lowest cost achievable for the production and distribution network after the merger if none of the plants is shut down? Which plants serve which markets?

c. What is the lowest cost achievable for the production and distribution network after the merger if plants can be scaled back or shut down in batches of 10 million units of capacity? Which plants serve which markets?

d. How is the optimal network configuration affected if all duties are reduced to 0? e. How should the merged network be configured?

e. How should the merged network be configured?