Oranges are grown picked and then stored in warehouses in Ta

Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload ($100s), supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago. Formulate this problem as a linear programming model, and solve using the computer.

Solution

Let a,b,c,d be the number of truck loads from Tampa to NY, Philadelphia, Chicago and Boston Resp.

Let x,y,0,z be the number of truck loads from Miami to NY, Philadelphia, Chicago and Boston Resp.

Let p,q,r,s be the number of truck loads from Fresno to NY, Philadelphia, Chicago and Boston Resp.

a+b+c+d <= 200

x+y+z <= 200

p+q+r+s <= 200

a+x+p>=130

b+y+q >=170

c+r >=100

d+z+s >=150

Shiping Cost = 9a+14b+12c +17d +11x+10y+10z +12p+8q+15r+7s