The following table is a transportation matrix showing the cost ($) per unit of shipping from Planti

i

to Distributorj

j

. 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 1Distributor 2Distributor 3SupplyPlant 182628510Plant 21510---390Plant 3181314150Demand500400140--

Letx

i

j

xij

= number units shipped from Planti

i

to Distributorj

j

Solve the transportation problem and use the result to fill the boxes below.

All answers are equally weighted.

a) At optimal solution:

x

11

=

x11=

x

12

=

x12=

x

13

=

x13=

x

21

=

x21=

x

22

=

x22=

x

23

=

x23=

x

31

=

x31=

x

32

=

x32=

x

33

=

x33=

Minimum Cost=

$

=$

(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