Answer
The expression of cost for the contractor to build the walls of a warehouse which have a floor area of $4000\text{ square feet}$ is $C\left( x \right)=475x+\frac{1400000}{x}$.
Work Step by Step
The expression of cost for the contractor to build the walls of a warehouse which have a floor area of $4000\text{ square feet}$ is $C\left( x \right)=475x+\frac{1400000}{x}$.a
Let the length of the warehouse be x and breadth of the warehouse be $y$.
Write the expression for the floor area of the warehouse.
$xy=4000$
Calculate y in terms of x.
$y=\frac{4000}{x}$
Write the expression for the cost of walls considering the cost to construct the outer wall is $\$175$ and for the inner wall is $\$125$.
$C=175\left( 2x+2y \right)+125x$
Substitute $\frac{4000}{x}$ for $y$.
$C=175\left[ 2x+2\left( \frac{4000}{x} \right) \right]+125x$
The cost is a function of x, so it can be expressed as,
$\begin{align}
& C\left( x \right)=175\left[ 2x+2\left( \frac{4000}{x} \right) \right]+125x \\
& C\left( x \right)=350x+\frac{1400000}{x}+125x \\
& =475x+\frac{1400000}{x}
\end{align}$
Hence, the expression of cost for the contractor to build the walls of a warehouse which have a floor area of $4000\text{ square feet}$ is $C\left( x \right)=475x+\frac{1400000}{x}$.
