Many airlines have restrictions on the the size of carry-on luggage. A com- mon requirement is that carry-on luggage must have a linear distance (sum of length, width, and height) of no more than 45 inches with an additional requirement of being able to slide under the seat in front of you. If we assume that the carry-on is a rect- angular box and one dimension is no more than half of one of the other dimensions (to ensure that it can slide under a seat), then what dimensions will maximize its volume?n
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