Ine Acine moget company has found that if widgets are priced at $$282,$ then $17000$ will be sold. They have also found that for every increase of $$16,$ there will be $700$ fewer widgets sold.

The marginal cost of widgets is $$112\mathrm{.}8.$ The fixed costs for the Acme Widget Company are $$12000.$

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: