Sleekfon and Sturdyfon are two major cell phone manufacturers that have recently merged. Their current market sizes are as shown in Table 5-9. 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/Australia. The capacity (in millions of units), annual fixed cost (in millions of $), and variable production costs ($ per unit) for each plant are as shown in Table 5-10. Transportation costs between regions are as shown in Table 5-11. 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, a variable production cost of $5.50, and a transportation cost of $2.20. The 25 USShipmentGermanyShipmentJapan Shipment Brazil Shipment India Shipment Demand(ton/yr)N. America 600 115 1,300 135 2,000 - 1,200 20 2,200 0 270 (0) S. America 1,200 - 1,400 - 2,100 - 800 190 2,300 - 190 - Europe 1,300 - 600 200 1,400 - 1,400 - 1,300 - 200 - Japan 2,000 - 1,400 120 300 - 2,100 - 1,000 - 120 - Asia 1,700 - 1,300 20 900 - 2,100 - 800 80 100 - Capacity (ton/yr) 185 115 475 475 50 - 210 210 80 80 Minimum Run Rate 93 238 25 105 40 $ Mark Yen Real Rs.Production Cost per Ton 10,000 15,000 1,800,000 13,000 400,000 Exch Rate 1.000 0.502 0.009 0.562 0.023 Prod Cost per Ton(US$) 10,000 7,530 16,740 7,306 9,200 Production Cost In US$ 1,150,000 3,576,750 - 1,534,260 736,000 Tpt Cost in US$ 69,000 489,500 - 176,000 64,000 Total 1,219,000 4,066,250 - 1,710,260 800,000 7,795,510 percent import duty is thus applied on $12.70 (5.00 + 5.50 + 2.20) to give a total cost on import of $15.88. For the questions that follow, assume that market demand is as in Table 5-9. The merged company has estimated that scaling back a 20-million-unit plant to 10 million units 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 only partially recovered because of severance and other costs associated with a shutdown. (a) What is the lowest cost achievable for the production and distribution network prior to the merger? Which plants serve which markets? Starting from the basic models in (a), we will build more advanced models in the subsequent parts of this question. Prior to merger, Sleekfon and Sturdyfon operate independently, and so we need to build separate models for each of them. Optimization model for Sleekfon: n = 3: Sleekfon production facilities. m = 7: number of regional markets. Dj = Annual market size of regional market j Ki = maximum possible capacity of production facility i cij = Variable cost of producing, transporting and duty from facility i to market j fi = Annual fixed cost of facility i xij = Number of units from facility i to regional market j. It should be integral and non-negative. 1 1 1niji1mijj1Subject tox 1 (5.1)x 1 (5.2)n n mi ij iji i jjiMin f c xD for j ,...,mK for i ,...,n Please note that we need to calculate the variable cost cij before we plug it into the optimization model. Variable cost cij is calculated as follows: