Hatcher Enterprises uses a chemical called Rbase in production operations at five divi- sions. Only six suppliers of Rbase meet Hatcher's quality control standards. All six sup- pliers can produce Rbase in sufficient quantities to accommodate the needs of each division. The quantity of Rbase needed by each Hatcher division and the price per gallon charged by each supplier are as follows:
|
Division
|
Demand (1000s of gallons)
|
Supplier
|
Price per Gallon ($)
|
|
1
|
40
|
1
|
12.60
|
|
2
|
45
|
2
|
14.00
|
|
3
|
50
|
3
|
10.20
|
|
4
|
35
|
4
|
14.20
|
|
5
|
45
|
5
|
12.00
|
|
|
|
6
|
13.00
|
The cost per gallon (in dollars) for shipping from each supplier to each division is provided in the following table:
|
Division
|
1
|
2
|
3
|
4
|
5
|
6
|
|
1
|
2.75
|
2.50
|
3.15
|
2.80
|
2.75
|
2.75
|
|
2
|
0.80
|
0.20
|
5.40
|
1.20
|
3.40
|
1.00
|
|
3
|
4.70
|
2.60
|
5.30
|
2.80
|
6.00
|
5.60
|
|
4
|
2.60
|
1.80
|
4.40
|
2.40
|
5.00
|
2.80
|
|
5
|
3.40
|
0.40
|
5.00
|
1.20
|
2.60
|
3.60
|
Hatcher believes in spreading its business among suppliers so that the company will be less affected by supplier problems (e.g., labor strikes or resource availability). Company policy requires that each division have a separate supplier.
a. For each supplier-division combination, compute the total cost of supplying the division's demand.
b. Determine the optimal assignment of suppliers to divisions.