The following table is a transportation matrix showing the profit ($) per unit realized by shipping from Plant i to Distributor j. The objective is to maximize profit 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 Plant 1 28 11 8 470 Plant 2 19 27 --- 310 Plant 3 13 23 22 150 Demand 460 360 100 Let zij = number units shipped from Plant i to Distributor j Solve the transportation problem and use the result to fill the boxes below. All answers are equally weighted. a) At optimal solution: 211= 450 #12 0 13= 0 121 0 231 0 x22= 360 223= 0 132 == 30 x 133= 80 x Maximum Profit 9980 b) At optimal solution, how much unused capacity is available at each Plant? Slack at Plant 1490 x units Slack at Plant 2 = 360 xunits Slack at Plant 3 = 110 x units