Module C Internet Homework Problems
C.18
The following table presents cost, capacity, and demand data for a transportation problem in
Stephanie Robbin’s furniture company. Set up the appropriate transportation table and find
the initial solution using northwest-corner data. Note that a “dummy” source is needed to
balance the problem.
From \ To
1
2
3
A
B
C
Demands
$30
$10
$20
40
$10
$10
$10
60
$5
$10
$25
55
Capacity
20
30
75
C.19 Determine whether the new solution table presented in Example C4 (see Figure C.8 in the text)
contains the optimal transportation allocation for Arizona Plumbing. If not, compute an improved solution
and test it for optimality.
C.20
After one iteration of the stepping-stone method, G. W. Willis Paint Company produced the
following transportation table. Complete the analysis, determining an optimal shipping solution.
G.W. Willis Paint Company
From \ To
Warehouse 1
Factory A
120
Warehouse 2
$8$ 8
Warehouse 3
$5$ 5
Factory
capacity
$$6 6
120
$ 15
$15
80
$ 10
$10
$$14
14
Factory B
80
$3$ 3
Factory C
30
Warehouse
requirements
150
$ 9
$9
80
Cost = $2,350
1
$$10
10
50
80
50
280
C.21 Sound Track Stereos assembles its high-fidelity stereophonic systems at three plants and distributes
them from three regional warehouses. The production capacities at each plant, demand at each
warehouse, and unit shipping costs are presented in the following table:
Sound Track Stereos
From \ To
Warehouse
WarehouseB A
Plant
Warehouse
supplyB
Warehouse C
Plant Capacity
Plant W
$6
$4
$9
200
Plant Y
$10
$5
$6
175
Plant Z
$12
$7
$8
75
Warehouse demand
250
100
150
500 \ 450
a) Set up this transportation problem by adding a dummy plant. Then use the northwestcorner rule to find an initial basic feasible solution.
b) What is the optimal solution?
C.22 Jim Lloyd, vice president for operations of HHN, Inc., a manufacturer of cabinets for telephone
switches, is constrained from meeting his 5-year forecast by limited capacity at the company’s three
existing plants. These plants are Waterloo, Pusan, and Bogota. As his able assistant, you have been told that
because of existing capacity constraints and the expanding world market for HHN cabinets, a fourth plant is
to be added. The real estate department has advised Lloyd that two sites seem particularly good because of
stable political situations and tolerable exchange rates. These two locations are Dublin, Ireland, and
Fontainebleau, France. Lloyd suggests that from the data in the following table, which provide production
and transportation costs, you should be able to determine where the fourth plant should be located. (Note:
This problem is degenerate with the data for both locations.)
Plant Location
MARKET AREA
Canada: Demand 4,000
Production cost
Transportation cost
South America: Demand 5,000
Production cost
Transportation cost
Pacific Rim: Demand 10,000
Production cost
Transportation cost
Europe: Demand 5,000
Production cost
Transportation cost
Capacity
WATERLOO
PUSAN
BOGOTA
FONTAINEBLEAU
DUBLIN
50
10
30
25
40
20
50
25
45
25
50
20
30
25
40
10
50
30
45
30
50
25
30
10
40
25
50
40
45
40
50
25
8,000
30
40
2,000
40
30
5,000
50
10
9,000
45
20
9,000
2