Montgomery Scott, Leonard McCoy, and Hikaru Sulu need to construct a rectangular tank to hold two (small) humpback whales22. The tank needs to hold 18, 000 cubic feet of water. The front and back sides of the tank are made of six inch think plexiglass which costs 324 dollars per square foot; the left and right sides are to be made of one inch aluminum which costs them 96 dollars per square foot, the bottom will be made of .025 inch thick titanium which costs 48 dollars per square foot; and the top is to be made of an extremely heavy polyester mesh that costs 6 dollars per square foot. Assuming no other constraints, what are the dimensions of the tank that minimize its cost?

600 feet length, 10 feet width and 3 feet height.

Step-by-step explanation:

Given the information in the question and assuming no other constraints than the ones that are mentioned, the dimensions of the tank that minimizes the cost should be the one that is the widest on the bottom because the material with the lowest cost per square foot is used at the bottom.

If we assume that the area of the bottom of the tank is 6000 square foot with dimensions of 600 feet length and 10 feet width. 600 feet should be the length because the material with the lowest cost after the titanium is the aluminum that is used for the left and right sides.

These dimensions suggest that the tank should have a height of 3 feet for it to meet the 18,000 cubic feet requirement.

According to the total dimensions of the tank with 600 feet length, 100 feet width and 3 feet height, the cost comes up to 288,000+345,600+19,440 = 653,040 $.

I hope this answer helps.

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