2) Chipset Logistics DXP is a manufacturer of various types of semiconductor chips, including telecom, automotive,...

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2) Chipset Logistics DXP is a manufacturer of various types of semiconductor chips, including telecom, automotive, and healthcare. The automotive business unit of the company is releasing their state-of-the-art advanced driver-assistance system chipset developed in the 3-nm CMOS technology. Besides producing at their own fab (fab1), they have outsourced the chipset production to two pure-play foundries (fab2 and fab3). The chipsets can be shipped to two plants of a car manufacturing customer (plant1 and plant2) either directly from the fabs or through two distribution centers (DC1 and DC2). The chipsets can move among fabs, between DCs, between plants, and from fabs (through DCs) to plants. The three fabs can produce at most 400K, 600K, and 200K packs of chipset, respectively (K-1000). The two plants demand exactly 400K and 180K packs of chipsets, respectively. The cost of shipment via each possible link is indicated in the table below. Note that due to administrative or economic reasons, the cost of bidirectional links are asymmetric. Because of reliability measures, at most 400K packs of chipset can be sent via any shipment link. fab2 fab1 DC1 fab3 DC2 Per pack cost of shipment via the links (in ). from to fabl fab3 DC1 DC2 plant1 plant2 fab2 fabl 100 60 100 100 400 400 fab2 180 180 20 20 160 300 fab3 8 160 20 10 200 240 DC1 24 40 240 DC2 16 40 240 plant1 20 plant2 140 [35 marks] ADAS plant1 plant2 Formulate and solve a mathematical program (MILP) to answer the following questions: 1. How many chipset packs should be sent via each link (and in which direction if applicable) to minimize the total shipment cost, while fulfilling demand of both plants? 2. How much is the minimum total shipment cost? 2) Chipset Logistics DXP is a manufacturer of various types of semiconductor chips, including telecom, automotive, and healthcare. The automotive business unit of the company is releasing their state-of-the-art advanced driver-assistance system chipset developed in the 3-nm CMOS technology. Besides producing at their own fab (fab1), they have outsourced the chipset production to two pure-play foundries (fab2 and fab3). The chipsets can be shipped to two plants of a car manufacturing customer (plant1 and plant2) either directly from the fabs or through two distribution centers (DC1 and DC2). The chipsets can move among fabs, between DCs, between plants, and from fabs (through DCs) to plants. The three fabs can produce at most 400K, 600K, and 200K packs of chipset, respectively (K-1000). The two plants demand exactly 400K and 180K packs of chipsets, respectively. The cost of shipment via each possible link is indicated in the table below. Note that due to administrative or economic reasons, the cost of bidirectional links are asymmetric. Because of reliability measures, at most 400K packs of chipset can be sent via any shipment link. fab2 fab1 DC1 fab3 DC2 Per pack cost of shipment via the links (in ). from to fabl fab3 DC1 DC2 plant1 plant2 fab2 fabl 100 60 100 100 400 400 fab2 180 180 20 20 160 300 fab3 8 160 20 10 200 240 DC1 24 40 240 DC2 16 40 240 plant1 20 plant2 140 [35 marks] ADAS plant1 plant2 Formulate and solve a mathematical program (MILP) to answer the following questions: 1. How many chipset packs should be sent via each link (and in which direction if applicable) to minimize the total shipment cost, while fulfilling demand of both plants? 2. How much is the minimum total shipment cost?