Strangely, the wine for a large wedding reception is to be

Problem 55

Strangely, the wine for a large wedding reception is to be served in a stunning cut-glass receptacle with the interior dimensions of 40 cm x 40 cm x 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. Purchasing a larger bottle instead of multiple smaller bottles decreases the overall cost of the wine. To minimize the cost, (a) which bottle sizes should be purchased and how many of each should be purchased and, once the receptacle is filled, how much wine is left over in terms of (b) standard bottles and (c) liters?

1 standard bottle

1 magnum 2 standard bottles

1 jeroboam 4 standard bottles

1 rehoboam 6 standard bottles

1 methuselah 8 standard bottles

1 salmanazar 12 standard bottles

1 balthazar 16 standard bottles 11.356 L

1 nebuchadnezzar 20 standard bottles

                                                          Step by Step Solution

Step 1 of 3

Volume of the receptacle

Since volume of , the no. of standard bottles needed to fill the receptacle  

(a) To minimise the cost the larger bottle is to be purchased, that’s 3 nebuchadnezzar and 1 methuselah to fill the receptacle.