H&C is a manufacturer of home appliances. H&C has plants in Country A, Country B, and Country C. The market is divided into four regions: North, East, South, and West. Plant capacities (millions of units per year), regional demand (millions of units), annual fixed costs (millions of $ per year), and variable production and shipping costs ($ per unit in each cell) are shown below: North East South West Capacity Annual fixed cost A 100 110 105 100 50 900 B 95 105 110 105 50 1000 C 90 100 115 110 40 850 Demand 30 20 20 35 Tax rates: Country A: 0.25; Country B: 0.2; Country C: 0.3 To maintain a certain utilization rate, the capacity used at each plant should be at least 40% of the max capacity. Each appliance sells for an average price of $300. All plants are profit centers, and the company pays taxes separately for each plant. (USE Simplex LP in the solver) What is the optimal network if the goal is to minimize the total annual cost? (5 points) What is the optimal network if the goal is to maximize total after-tax profits? (5 points) Hint: after-tax profit of each plant =