A company has found that the marginal cost $($in thousands of dollars$)$ to produce $x$ central air conditioning units is $C^{\text{'}}(x)=\frac{56x}{4x^2+e},$ where $x$ is the number of units produced

$($a$)$ Find the cost function, given that the company incurs a fixed cost of $$10,000$ even if no units are built.

$($b$)$ The company will seek a new source of investment income if the cost is more than $$18,000$ to produce $5$ units. Should they seek this new source?

$($a$)$ What substitution should be used to determine the cost function?

Use the quantity as the substitution, $u=,,$ so that $du=1,$ dx