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Anna35 [415]
3 years ago
11

A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 998.25 cubic fe

et. The cost of wall paint is $0.12 per square foot and the cost of ceiling paint is $0.18 per square foot. Find the room dimensions that result in a minimum cost for the paint. g

Mathematics
1 answer:
AlladinOne [14]3 years ago
6 0

Answer:

the room dimensions that result in a minimum cost for the paint is;

x = 11 ft

y = 11 ft

z = 8.25 ft

Step-by-step explanation:

Shown in the attachment;

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AX  = b or  \left[\begin{array}{cc}1&1\\0.1&0.05\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]  = \left[\begin{array}{c}15\\1.10\end{array}\right]

<h3>The above matrix can be used to determine the number of dimes  x and  nickels y.</h3>

Step-by-step explanation:

Here, total number of coins  = 15

Let us assume the number of dimes  = x

Also, let us assume the number of nickels  = y

So, x + y = 15  .... (1)

Again, 1 dime  = $0.1

So, x dimes  = x ($0.1)   = $ (0.1 x)

1 nickel  = $0.05

So, y nickels  = y ($0.05)   = $ (0.05 y)

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⇒  0.1 x + 0.05 y  = 1.10     .... (2)

So, from (1) and (2) the matrix can be written as:

AX  = b or  \left[\begin{array}{cc}1&1\\0.1&0.05\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]  = \left[\begin{array}{c}15\\1.10\end{array}\right]

The above matrix can be used to determine the number of dimes  x and  nickels y.

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