Price, Demand, and Total Cost for Widget Production Demand x (widgets) Price p ($/widget) Total Cost C($) 141 609 133 1103 1618 2109 2603 3111 3619 4103 4601 5114 Recall that profit can be computed in terms of revenue and cost. Assume that the annual widget sales match the annual widget demand and annual widget production. Construct a model for profit using the models for revenue and cost that you found in the Revenue and Cost sections. Give your model for profit LaTeX: P(x)P ( x ), where LaTeX: P(x)P ( x ) is the total annual profit in dollars for LaTeX: xx widgets sold.
Plot your models for cost, revenue, and profit on the same graph. Adjust the max/min to display the data in a reasonable way. On the plot, be sure to
Make a title for the plot "Total Cost, Revenue, and Profit".
Label your axes. Label the horizontal axis "Annual widget production", and label the vertical axis "Total cost/revenue/profit of producing widgets ($)".
Label the graphs or include a legend to make it clear which graph is which. What are the break-even points?
-What is the profit at the break-even points? Be sure to answer in complete sentences and to include units. Explain how you found the results.
What number of widgets sold will yield positive profit? Be sure to answer in complete sentences and to include units. Explain how you found the results.
Determine the number of widgets that you should try to sell in order to maximize profit. What is the maximum profit? Be sure to answer in complete sentences and to include units. Explain how you found the results.