Question: A manufacturer of micro-laptops models its corporate profit with the following function, where x is the number of units sold:

\(P\left( x \right)=-10{{x}^{2}}+36000x-45000\)

(a) Determine the corporate profit if 1500 micro-laptops are sold.

(b) Determine the corporate profit if 2000 micro-laptops are sold.

(c) Determine the corporate profit if 2500 micro-laptops are sold.

(d) Determine the maximum profit and the number of micro-laptops that must be sold in order to achieve that maximum profit. [COMMENTS & HINTS: For full credit, explain or justify your answer, using both pre-calculus (e.g., data table or graph) and calculus (e.g., marginals and derivatives) methods.]