Problem $2$: $(8$ pts$.)$: A home renovation company charges for wooden flooring installation based on the amount of square footage covered. The marginal cost, $C^{\text{'}}(x),$ which represents the cost $($in dollars$)$ to install each additional square foot of wooden flooring beyond $x$ square feet, is given by the following function:

$C^{\text{'}}(x)=5x+75$

The company has a base installation charge of $$300($which covers small areas up to $75$ square feet$).$ This base fee will be considered a constant when integrating the marginal cost to find the total cost for larger areas.

a$.$ Calculate the total cost of installing $300$ square feet of wooden flooring.

b$.$ After installing the initial $300$ square feet, the client decides to add an extra $50$ square feet to the project. Find the additional cost for this extra work.

c$.$ Find the new total cost for the installation of $350$ square feet of wooden flooring in light of the additional work.

SOLUTION: