Answer the following questions using above data: 1.

2.

Use the case below to answer the question(s). Rolling Inc. produces cars at two plants: Baltimore, Maryland, and Orlando, Florida. They ship them to major distribution centers in Minnesota, Dallas, Los Angeles, and Memphis. The Accounting, Production, and Marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Plant Baltimore Orlando Demand Minnesota $25.20 $19.50 300 Distribution Center Dallas Los Angeles Memphis $28.70 $23.04 $35.16 $32.52 $16.22 $35.84 700 1,000 2,000 Capacity 1.200 800 Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas. Both plants would have a capacity of 3,000 units but only one can be built. The table below shows the revised data. Plant Baltimore Orlando Ohio Kansas Demand Distribution Center Minnesota Dallas Los Angeles Memphis Capacity $25.20 $28.70 $23.04 $35.16 2,400 $19.50 $32.52 $16.22 $35.84 1,600 $20.82 $23.08 $19.74 $23.28 3,000 $27.76 $33.90 $25.02 $16.36 3,000 600 1.000 1,400 3.600 Define Xij = amount shipped from plant i to distribution centerj, where i = 1 represents Baltimore, and j = 1 represents Minnesota. Define a binary variable for the decision of which plant to build: Y1 = 1 if the Ohio plant is built, and Y2 = 1 if the Kansas plant is built. To guarantee that only one new plant is built, we must have the constraint OY1+ Y21 O Y1 + Y2 = 1 O Y1 + Y2 s 1 O Y1 > 1 The inequality/equality that explains the demand constraint for Minnesota is X11 + X12 + X13 + X14 600 X11 + X21 2 600 X11 + X12 + X13 + X14 = 600 O X11+X21 + X31 + X41 = 600