Question 1116821: An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist wants the words to all be horizontal in the final mosaic. The word tiles come in two sizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
The largest allowed dimensions are 4 ft tall by 6 ft wide, which is 48 in tall and 72 in wide.
The smallest allowed dimensions are 3 ft tall by 5 ft wide, which is 36 in tall and 60 in wide.
Two things are obvious:
1. Than smaller the total size of the final mosaic is, than it is cheaper.
2. Than greater the number of large tiles is, than the mosaic is cheaper.
Therefore, the cheapest solution is this:
Place 6 x 5 large tiles (6 vertically and 5 horizontally) to cover the rectangle of the size
6*6 = 36 inches vertically
and 12*5 = 60 inches horizontally.
All conditions will be satisfied, and the cost will be minimal, which is OBVIOUS.
So, you need 6*5 = 30 large tiles (and 0 small tiles).
The minimal cost will be $4.50*6*5 = $135.
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