$[30$ points$]$ Refer the Capacitated Facility Location Model in presentation $8.$ The transportation costs, demand, fixed cost of each low and high$-$capacity plants is changed as follows:

$\backslash$table$[[$Inputs $-$ Costs, Capacities, Demands$],[,\backslash$table$[[$Demand Region$],[$Production and Transportation Cost per $1,000,000$ Units$]],$Fixed,Low,Fixed,High$],[\backslash$table$[[$Supply$],[$Country$]],\backslash$table$[[$N$.],[$America$]],$S$.$ America,Europe,Asia,Africa,$\backslash$table$[[$Cost$],[($$$)]],$Capacity,$\backslash$table$[[$Cost$],[($$$)]],$Capacity$],[$USA$,82,96,110,130,115,6,500,10,12,000,25],[$Brazil$,97,79,112,115,106,4,800,10,7,750,20],[$Germany$,105,114,93,108,99,6,500,10,11,750,20],[$China$,115,125,100,65,84,4,500,12,8,150,20],[$Nigeria$,132,110,100,98,69,4,000,12,8,000,20],[$Demand$,15,12,16,20,12.,-,-,-,-]]$

a$.$ Which facilities should be operated? Which size? What are the shipped quantities to each demand region from each supply country? What is the total operating cost?

b$.$ The firm is considering to add a new facility in Sri Lanka, which has a capacity of $20($million$)$ units. The fixed cost of the facility would be $$7500.($A low capacity plant is not an option for Sri Lanka.$)$ Transportation cost from Sri Lanka to the demand regions are as follows:

$\backslash$table$[[$Supply Country,N$.$ America,S$.$ America,Europe,Asia,Africa$],[$Sri Lanka,$125,135,95,70,75]]$

Modify the LP and solve the problem again. Which facilities should be operated? Which size? What are the shipped quantities to each demand region from each supply country? What is the total operating cost?