Set up a balanced initial blank chart for the "Sparkle Plenty" problem. There is no need to enter a starting solution. Hint: Some transportation problems may require an extra row and column to balance them. The Sparkle Plenty Problem The Sparkle Plenty Diamond Company has orders from three cities as follows: Kuwait, 3500 karats; Paris, 8000 karats; New York, 7000 karats. Its diamond-cutting centers can produce diamonds in the following quantities: Antwerp, 6,500 karats; Rotterdam, 5,000 karats, New York, 4,500 karats. The shipping costs (in dollars per karat) are given in the following table: From To Kuwait Paris New York Antwerp 90 30 90

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Set up a balanced initial blank chart for the “Sparkle Plenty" problem. There is no need to enter a
starting solution. Hint: Some transportation problems may require an extra row and column to
balance them.
The Sparkle Plenty Problem
The Sparkle Plenty Diamond Company has orders from three cities as follows: Kuwait, 3500
karats; Paris, 8000 karats; New York, 7000 karats. Its diamond-cutting centers can produce
diamonds in the following quantities: Antwerp, 6,500 karats; Rotterdam, 5,000 karats, New York,
4,500 karats. The shipping costs (in dollars per karat) are given in the following table:
From
To
Kuwait
Paris
New York
Antwerp
90
30
90
Rotterdam
80
20
80
New York
120
100
50
The company also has another outside source – the AKV center in Johannesburg, South Africa,
but there are some restrictions on this source. First, AKV sets its shipping rate to a given city
equal to the highest rate charged by any of the cutting centers to that city. Also, AKV will only
produce quantities of cut diamonds in multiples of 1,000 karats. Diamonds may be stored in
secure vaults at each center at the following rates per karat: Antwerp, $40; Rotterdam, $50, New
York, $70, Johannesburg, $20; these charges are paid by Sparkle Plenty, if necessary. The
problem, naturally, is to minimize total shipping and storage costs.
Transcribed Image Text:Set up a balanced initial blank chart for the “Sparkle Plenty" problem. There is no need to enter a starting solution. Hint: Some transportation problems may require an extra row and column to balance them. The Sparkle Plenty Problem The Sparkle Plenty Diamond Company has orders from three cities as follows: Kuwait, 3500 karats; Paris, 8000 karats; New York, 7000 karats. Its diamond-cutting centers can produce diamonds in the following quantities: Antwerp, 6,500 karats; Rotterdam, 5,000 karats, New York, 4,500 karats. The shipping costs (in dollars per karat) are given in the following table: From To Kuwait Paris New York Antwerp 90 30 90 Rotterdam 80 20 80 New York 120 100 50 The company also has another outside source – the AKV center in Johannesburg, South Africa, but there are some restrictions on this source. First, AKV sets its shipping rate to a given city equal to the highest rate charged by any of the cutting centers to that city. Also, AKV will only produce quantities of cut diamonds in multiples of 1,000 karats. Diamonds may be stored in secure vaults at each center at the following rates per karat: Antwerp, $40; Rotterdam, $50, New York, $70, Johannesburg, $20; these charges are paid by Sparkle Plenty, if necessary. The problem, naturally, is to minimize total shipping and storage costs.
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