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

24 12 11 470

Plant 1

Plant 2 17 22 --- 370

Plant 3 13 19 18 200

Demand 450 420 150 .....

-- Let xij = 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: x11= x12= x13= x21= x22= x23= x31= x32= 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 = units?

Slack at Plant 3 = units?