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 2. Distributor 1 Distributor 2 Distributor 3 Supply Plant 1 23 26 13 430 Plant 2 12 --- 27 580 Plant 3 28 22 15 460 Demand 490 400 510 Let my = 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: $11 = I21 TH = I31 Maximum Profit = $ b) At optimal solution, how much unused capacity is available at each Plant? Slack at Plant 1 = units Slack at Plant 2 = units Slack at Plant 3 = units