Question

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

@ganeshie8

Answer 2

It's also a linear programing word problem. I'm looking for constraints. t.t

Answer 3

I have been looking around for a correct answer and it is " 0 small tile, 6 large tiles; minimum cost $27"

Answer 4

Please hold on, I'm reviewing my work and yours to get the ideas of the problem. =)

Answer 5

Let call "y" for lager tiles
Let call "x" for small tiles
Let call "z" the minimize cost
Therefore, we will have the following objective function.

z = 3.50x + 4.50y

Answer 6

\[ \le (4ft)tall (6ft)wide\]
\[ \ge (3ft)tall (5ft)wide\]
smaller tiles (4in)tall (4in)wide
large tiles (6in)tall (12in)wide

This is the information i am getting, but i know i'm missing 2 variables before:
\[ \le (4ft)tall (6ft)wide\]
\[ \ge (3ft)tall (5ft)wide\]

Answer 7

@ganeshie8

Answer 8

@ganeshie8

Answer 9

z = 3.5x + 4.5y

x*(4/12)*(4/12) + y*(6/12)*(12/12) <= 6*4
x*(4/12)*(4/12) + y*(6/12)*(12/12) >= 5*3

http://www.wolframalpha.com/input/?i=minimize+3.5x+%2B+4.5y%2C++x*%284%2F12%29*%284%2F12%29+%2B+y*%286%2F12%29*%2812%2F12%29+%3C%3D+6*4%2C+x*%284%2F12%29*%284%2F12%29+%2B+y*%286%2F12%29*%2812%2F12%29+%3E%3D+5*3%2Cx%3E%3D0%2Cy%3E%3D0

Answer 10

0 small tiles
30 large tiles

minimum cost = 135

Answer 11

the answer you have posted in the start of thread is wrong.

Answer 12

Yah dear, http://openstudy.com/study#/updates/521b817ce4b06211a67d3048

In this post, the writer said he got " 0 point" from his teacher. Besides, i believe we go to the same school =P

Answer 13

He got the wrong answer because: 1) He did not graph it, his method made him confused :P