(Solved): A manufacturer believes that the cost function C(x)=25x2+115x+800 approximates the dollar cost ...

A manufacturer believes that the cost function $C(x)=\frac{5}{2}{x}^2+115x+800$ approximates the dollar cost of producing $x$ units of a product. The manufacturer believes it cannot make a profit when the marginal cost goes beyond $\$415$. What is the most units the manufacturer can produce and still make a profit? What is the total cost at this level of production? The manufacturer can make up to units and still make a profit. This leads to a total cost of $\$$