The wine for a large European wedding reception is to be served in a stunning cu

Question

The wine for a large European wedding reception is to be served in a stunning cut-glass receptacle with the interior dimensions of 40 cm 40 cm 30 cm (height). The receptacle is to be initially filled to the top. The wine can be purchased in bottles of the sizes given in the following table, where the volumes of the larger bottles are given in terms of the volume of a standard wine bottle. Purchasing a larger bottle instead of multiple smaller bottles decreases the overall cost of the wine.

1 standard
1 magnum = 2 standard
1 jeroboam = 4 standard
1 rehoboam = 6 standard
1 methuselah = 8 standard
1 salmanazar = 12 standard
1 balthazar = 16 standard = 11.356 L
1 nebuchadnezzar = 20 standard


(a) To minimize that overall cost, which bottle sizes should be purchased and how many of each should be purchased?
__ standard
__ magnum
__ jeroboam
__ rehoboam
__ methuselah
__ salmanazar
__ balthazar
__ nebuchadnezzar
(b) How much wine is left over once the receptacle is filled?
__ L

Explanation / Answer

If the receptacle is 40 by 40 by 30 it is 48,000 ccs or 48 litres. 1 standard bottle is 11.356/16= .70975 litre. So 1 neb is 14.195 litres, and we should get three of those which will be 42.585 litres. That leaves 5.415 litres left over, so we should get 1 reh at 6 for 4.2585 litres. Now we have 5.415-4.5285= 1.1565, so we should get 1 magnum which will fill it. 3 neb, 1 reh, 1 mag.

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