The Acme Widget Company has found that if widgets are priced at $ 161, then 1000 will be sold. They have also found that for every increase of $ 12, there will be 800 fewer widgets sold.
The marginal cost of widgets is $ 120.75. The fixed costs for the Acme Widget Company are $ 6000.

If $x$ represents the price of a widget find the following in terms of $x$:

The number of widgets that will be sold:

The revenue generated by the sale of widgets:

The cost of producing just enough widgets to meet demand:

The profit from selling widgets:

Find the price that will maximize profits from the sale of widgets: