The following table is a transportation matrix showing the cost ($) per unit of shipping from Plant ii to Distributor ij. The objective is to minimize shipping costs while meeting the demand placed by each Distributor. There is no shipment between Plant 2 and Distributor 3. Distributor 1 Distributor 2 Distributor 3 Supply 9 11 570 24 340 17 16 460 550 500 250 Plant 1 Plant 2 Plant 3 Demand 27 10 23 Let xixij = number units shipped from Plant ii to Distributor jj solve the transportation problem and use the result to fill the boxes below. All answers are equally weighted. a) At optimal solution: 550 x115x115 x12=x12=1 X21=x21=1 X22=X22= x315x31=1 x32=X32= Minimum Cost =$=$ X135x13= x235x23=1 X33=x33= b) At optimal solution, how much unused capacity is available at each Plant? Slack at Plant 1 Slack at Plant 2 = Slack at Plant 3 units units units