The table below contains the price, demand, and total cost data for the production ofx widgets.Herep is the price (in dollars) of a widget for an annual demand ofxwidgets, andCis the annual total cost (in dollars) of producingxwidgets per year.

Demandx Pricep Total Cost C

($/widget) (widgets)

10 141 609

20 133 1103

30 126 1618

40 128 2109

50 113 2603

60 97 3111

70 90 3619

80 82 4103

90 79 4601

100 53 5114

1 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 profitP(x)

, whereP(x)

is the total annual profit in dollars forx

widgets sold.

2 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.

3 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.

4 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.

5 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.