Problem $1$: $(6$ points$)$ Suppose a company manufactures a product, and the marginal cost $($the cost to produce one additional unit$)$ of the product depends on the number of units produced, denoted by $x.$ The marginal cost function is given by $C^{\text{'}}(x)=3x^2-7$ dollars per unit, where $x$ is measured in hundreds of units.

The company wants to increase its production from $100$ units $(1$ hundreds of units$)$ to $400$ units $(4$ hundreds of units$).$ Using left endpoint Riemann Summation, estimate the total additional cost the company will incur for increasing the production within this range. Assume we divide the interval from $1$ to $4$ into $n$ equally spaced subintervals. Set up$,$ but do not solve, a Riemann Sum using Sigma Notation ${\displaystyle \underset{i=1}{\overset{n}{}}}f(c_k)x_k.$ Leave the Riemann Sum as your final answer and express your answer in hundreds of units $($i$.$e$.,$ use $1$ for $"100"$ and $4$ for $"400"$ where the abbreviations are implicitly understood.$)$