Super Products Inc. has three plants, located at Aville, Bville,and Cville, producing shipments of its new wonder trouser-presswhich have to be shipped to four retail centers. The plants atAville, Bville, and Cville produce 12, 17, and 11 shipments oftrouser-presses per week, respectively. Each retail center needs toreceive 10 shipments per week. The distance from each plant to eachretail center in kilometers is as follows:

                                                            Retail Center

                                              1             2             3             4

                         Aville        800        1300        400          700

Plant                 Bville      1100        1400        600         1000

                         Cville        600        1200        800          900

Shipping costs per shipment are $100 plus 25 cents perkilometer. Super Products Inc. wishes to design an optimal shippingplan to minimize costs.

i) Set up an appropriate transportation problem

ii) Determine an initial basic feasible solution using the VogelMethod and then solve the problem using the transportation simplex.Be sure to compute not only the required pattern of shipments butalso the actual minimum cost of making them.

iii) How would your solution change if the cost of shipmentsbetween Bville and Retail Center 3 became prohibitively expensive?Explain.