Tax rates: Country A: $0\mathrm{.}25$: Country B: $0\mathrm{.}2$: Country C: $0\mathrm{.}3$

To maintain a certain utilization rate. the capacity used at each plant should be at least $50\%$ of t he maximum capacity.

Each appliance sells for an average price of $$300.$ All plants are profit centers. and t he company pays taxes separately for each plant. $($USE Simplex LP in the solver$)$

What is t he optimal network if the goal is to minimize the total annual cost?

What is t he optimal network if the goal is to maximize total after$-$tax profits? Hint: after$-$tax profit of each plant$=$ annual profit of each plant$(1-$tax rate$)$: annual profit$=$ revenue $-$ fixed cost

$-$ total production and transportation costs

Should both answers be the same or not$>$ Why?