Please only answer this question using text so that I can better understand it.
ID: 2911379 • Letter: P
Question
Please only answer this question using text so that I can better understand it.
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? Show your work.
Explanation / Answer
The small tiles are 1/3 ft square, so have an area of 1/9 ft^2. Their cost is
.. ($3.50/tile) / (1/9 ft^2/tile) = $31.50/ft^2
The small tiles are 1/2 ft by 1 ft, so have an area of 1/2 ft^2. Their cost is
.. ($4.50/tile) / (1/2 ft^2/tile) = $9.00/ft^2
Clearly, cost will be minimized if the larger tiles are used exclusively.
It will take 6 of the larger tiles to make a mosaic that is 1 ft wide by 3 ft high. It will take 5 of those to cover the minimum area of 3 ft high by 5 ft wide, thus 6*5 = 30 large tiles.
You can figure the cost either of two ways.
.. 30 tiles * $4.50/tile = $135.00
.. (3 ft)*(5 ft)*($9.00/ft^2) = $135.00
The minimum cost mosaic is 30 large tiles at a cost of $135.00.