Question

19 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 1

Total tiles need - 30 large tiles and 0 small tiles

Minimum cost is $135

Explanation:

Allow dimensions are
`4 ft(48 inc) tall * 6 ft(72 inch) wide.`

Smallest allowed dimensions are
`</p><p>3 ft(36 inch) tall  * 5 ft (60 inch) wide,`

2 things need to be noticed

1. smaller thee total size of final mosaic, cheaper the cost

2. Greater thee number of large tiles, cheaper the mosaic

Place
`6 * 5- large\ tiles (i.e 6\ vertically\ &\ 5 horizontally)` to fully cover the size of rectangle

`6* 6 = 36 inches vertically`

and
`12* 5 = 60 inches horizontally`

.

Therefore,total tiles need

`6* 5 i.e. 30\ large\ tiles` (& 0 small tiles).

The minimal cost is
`$4.50* 6* 5 = $135.`