Question

Which of the following expression correctly represent the overall cost of a roof system 'C'.
$[\text{s = spacing of the trusses and}{k}_1,k_2,k_3\text{are constants}]$

Answer 1

$\text{The cost of trusses}\propto \frac{1}{s}$
$\Rightarrow C_t=\frac{k_1}{s}$

$\text{The cost of purlins}\propto s^2$
$\Rightarrow C_p=k_2.s^2$

$\text{The cost of roof sheeting}\propto s$
$\Rightarrow C_r=k_3.s$

$\therefore \text{Total cost,}C=C_t+C_p+C_r$

$\therefore C=k_1/s+k_2.s^2+k_3.s$

$\text{Since}{k}_{1,},k_2,k_3\text{are constants.}\text{They can be interchangeable.}$