Scenario 3: A manufacturer is considering alternatives for building new plants in order to be located closer to three of its primary customers, with whom it intends to develop long-term relationships. The net cost of manufacturing and transporting each unit of the product to the customers will vary depending on where the plant is built and its production capacity. These costs are summarized in the following table: Supply Cost in $ per Unit Plant Customer A Customer B 30 40 Customer C 45 TTTT 35 2 45 3 70 4 20 5 65 65 50 50 45 25 45 45 The annual demand for products from customers A, B, and C is expected to be 40,000. 25,000, and 35,000 units, respectively. The construction cost and annual production capacity for each plant are: Construction Production Plant 1 Cost $1,325,000 40,000 Capacity 2 $1,100,000 30,000 3 $1,500,000 50,000 4 $1,200,000 20,000 5 $1,400.000 40,000 Write and solve a linear optimization model to help the company determine which plants to build in order to satisfy customer demand at minimum total cost. 9. What is the total cost? (in dollars) 10. How many plants are built? 11. How many units are being made at plant 2? 12. How many units is plant 1 shipping to custober B?