Reference no: EM13492505
Sindbad Marine Co has two ships Barbarossa and Jebel Tarik based in Lattaquieh. Each ship has three sections: front, middle, and back. Sinbad Marine Co has received an offer to transport two commodities: flour and tea. It can accept all or part of them. The following table indicates data on both commodities.
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Commodity
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Quantity ( t)
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Volume (m3)
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Fare (Dhs/t)
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Flour
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12,000
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1,5
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400
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|
Tea
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4,000
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4
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1,100
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The distribution of the tonnage according to the three sections for each ship is as follows (in t):
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Ship
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Front
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Middle
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Back
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Barbarossa
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1,500
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4,000
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3,000
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Jebel Tarik
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1,000
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3,000
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1,500
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The volume for each ship expressed in m3.
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Ship
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Front
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Middle
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Back
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Barbarossa
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2,500
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8,000
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5,000
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Jebel Tarik
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2,000
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7,000
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3,500
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In order to stabilize the ship, the weight in each section must be proportional to the tonnage. How must Sinbad Marine Co load both ships?
Answer:
The objective is to minimize the cost of shipping
Xji= Quantity (in ton) of flour shipped in section i of ship j
Yji = Quantity (in ton) of tea shipped in section i of ship j
i= 1 for the front section, i=2 for the middle section, i=3 for the back section
j= 1 for Barbarossa, j=2 for Jebel Tarik
The objective function Z = 400 (X11+ X12+ X13+ X21+ X22+ X23) + 1100 (Y11+ Y12 + Y13 + Y21 + Y22 + Y23)
Constraints:
- Flour (Barbarossa & Jebel Tarik): X11 + X12 + X13 + X21 + X22 + X23 ≤ 12000
- Tea (Barbarossa & Jebel Tarik): Y11+ Y12 + Y13 + Y21 + Y22 + Y23 ≤ 4000
- Barbarossa_Front_Qynt: X11 + Y11 ≤ 1500
- Barbarossa_Middle_Qynt:X12 + Y12 ≤ 4000
- Barbarossa_Back_Qynt:X13 + Y13 ≤ 3000
- JebelTarik_Front_Qynt:X21 + Y21 ≤ 1000
- JebelTarik_Middle_Qynt: X22 + Y22 ≤ 3000
- JebelTarik_Back_Qynt: X23 + Y23 ≤ 1500
- Barbarossa_Front_Vol: 1.5X11 + 4Y11 ≤ 2500
- Barbarossa_Middle_Vol: 1.5X12 + 4 Y12 ≤ 8000
- Barbarossa_Back_Vol: 1.5X13 + 4 Y13 ≤ 5000
- JebelTarik_Front_Vol: 1.5 X21 + 4Y21 ≤ 2000
- JebelTarik_Middle_Vol: 1.5 X22 + 4 Y22 ≤ 7000
- JebelTarik_Back_Vol: 1.5 X 23 + 4 Y23 ≤ 3500
- Xji<= 0, Yji <=0
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