Optimization: You and your classmates have decided to enter an ice sculpting contest. Before you begin, you must create a block of ice with the following strict requirements: 1. The volume must be 18 ft3. 2. The length of the base must be three times the size of the width of the base. 3. The long side of the base cannot be more than 12 ft long. 4. The short side of the base must be at least 1 foot long. (There are no constraints of the height of the block.) Find the dimensions of the ice block with the largest possible surface are. Note that your team captain will require proof that you have, indeed, provided a block with the maximum surface area.

Question

Optimization:

You and your classmates have decided to enter an ice sculpting contest. Before you begin, you must create a block of ice with the following strict requirements:

1. The volume must be 18 ft3.

2. The length of the base must be three times the size of the width of the base.

3. The long side of the base cannot be more than 12 ft long.

4. The short side of the base must be at least 1 foot long. (There are no constraints of the height of the block.)

Find the dimensions of the ice block with the largest possible surface are. Note that your team captain will require proof that you have, indeed, provided a block with the maximum surface area. 

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