a) At optimal solution: $11 = X12 = C13 C21 22 T 23 X31 = X33 Maximum Profit = $ b) At optimal solution, how much unused capacity is available at each Plant? Slack at Plant 1 = units Slack at Plant 2 = unitsThe following table is a transportation matrix showing the prot {1;} per unit realized by shipping from Plant 3' to Distributor 3'. 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 27 14 13 450 Plant 2 18 25 --- 370 Plant 3 1 5 22 1 9 100 Demand 41 O 400 70 - Let xi:- = number units shipped from Plant 1' to Distributorj Solve the transportation problem and use the result to fill the boxes below. All answers are equally weighted