A manufacturer of wireless gaming keyboards is preparing to set the price on a new model. Demand $($D$)$ is thought to depend on the price $($P$)$ and is represented by the model: D $=1800-3$P

The accounting department estimates that the total costs $($C$)$ can be represented by C $=4800+4$D

Develop a model for the total profits $($Revenues minus Costs$)$ and represent it on an Excel spreadsheet. Consider demands as units sold. Create columns for price, demand, revenue, costs, and profits. Use a table and a graph with $ on the y$-$axis and Demand on the x$-$axis to find the price at which profit is maximized.

Build a column in Excel for Price and consider price in $$10$ increments from $$50$ to $$600.($The column should have $$50,$ $$60,$ $$70,$ $$80,$ etc. all the way to $$600.)$

$1)$ At what price for the gaming keyboards is projected demand minimized?

$2)$ At what price for the gaming keyboards is projected demand maximized?

$3)$ At what price for the gaming keyboards is projected revenue maximized?

$4)$ At what price for the gaming keyboards is projected profit maximized?